two equal roots quadratic equation

So, in the markscheme of this question, they take the discriminant ( b 2 + 4 a c) and say it is greater than 0. This cookie is set by GDPR Cookie Consent plugin. Therefore, Width of the rectangle = x = 12 cm, Thanks a lot ,This was very useful for me. When roots of quadratic equation are equal? Once the binomial is isolated, by dividing each side by the coefficient of $a$, then the Square Root Property can be used on $(x-h)^{2}$. Subtract $3$ from both sides to isolate the binomial term. Therefore, we have: Use the method of completing the square to solve the equation $latex -x^2+3x+1=-2x^2+6x$. When we have complete quadratic equations of the form $latex ax^2+bx+c=0$, we can use factorization and write the equation in the form $latex (x+p)(x+q)=0$ which will allow us to find its roots easily. But even if both the System of quadratic-quadratic equations The solutions to a system of equations are the points of intersection of the lines. For the given Quadratic equation of the form, ax + bx + c = 0. Your Mobile number and Email id will not be published. What are the 7 steps in solving quadratic equation by completing the square?Isolate the number or variable c to the right side of the equation.Divide all terms by a (the coefficient of x2, unless x2 has no coefficient).Divide coefficient b by two and then square it.Add this value to both sides of the equation. Furthermore, if is a perfect square number, then the roots will be rational, otherwise the roots of the equation will be a conjugate pair of irrational numbers of the form where. WebTo do this, we need to identify the roots of the equations. Which of the quadratic equation has two real equal roots? In the graphical representation, we can see that the graph of the quadratic equation having no real roots does not touch or cut the $x$-axis at any point. The sum of the roots of a quadratic equation is + = -b/a. We will factor it first. We know that quadratic equation has two equal roots only when the value of discriminant is equal to zero. Expert Answer. Therefore, k=6 This equation does not appear to be quadratic at first glance. Could there be a quadratic function with only 1 root? Therefore, we have: We see that it is an incomplete equation that does not have the term c. Thus, we can solve it by factoring x: Solve the equation $latex 3x^2+5x-4=x^2-2x$ using the general quadratic formula. How to save a selection of features, temporary in QGIS? Analytical cookies are used to understand how visitors interact with the website. The cookie is used to store the user consent for the cookies in the category "Analytics". The discriminant of a quadratic equation determines the nature of roots. The standard form of a quadratic equation is: ax 2 + bx + c = 0, where a, b and c are real numbers and a != 0 The term b 2; - 4ac is known as the discriminant of a quadratic equation. If $p(x)$ is a quadratic polynomial, then $p(x)=0$ is called a quadratic equation. Take a look at these pages: 20 quadratic equation examples with answers, Solving Quadratic Equations Methods and Examples, How to Solve Quadratic Equations? Two parallel diagonal lines on a Schengen passport stamp. Solving Word Problems involving Distance, speed, and time, etc.. $a=5+2 \sqrt{5}\quad$ or $\quad a=5-2 \sqrt{5}$, $b=-3+4 \sqrt{2}\quad$ or $\quad b=-3-4 \sqrt{2}$. @IAmAGuest "What you get is a sufficient but not necessary condition" : did you intend "a necessary but not sufficient condition"? To complete the square, we take the coefficient b, divide it by 2, and square it. A quadratic equation has two equal roots, if?, a detailed solution for A quadratic equation has two equal roots, if? This is due to the fact that we will always get a zero root when c = 0: ax2 + bx + c = 0. Note that the product of the roots will always exist, since a is nonzero (no zero denominator). WebFind the value of so that the quadratic equation (5 6) = 0 has two equal roots. If in equation ax 2+bx+c=0 the two roots are equalThen b 24ac=0In equation px 22 5px+15=0a=p,b=2 5p and c=15Then b 24ac=0(2 5p) 24p15=020p Embiums Your Kryptonite weapon against super exams! The roots of an equation can be found by setting an equations factors to zero, and then solving each factor individually. To do this, we need to identify the roots of the equations. Therefore, the equation has no real roots. Solve Study Textbooks Guides. Where am I going wrong in understanding this? Many real-life word problems can be solved using quadratic equations. D > 0 means two real, distinct roots. Since $7$ is not a perfect square, we cannot solve the equation by factoring. In a quadratic equation $a{x^2} + bx + c = 0,$ there will be two roots, either they can be equal or unequal, real or unreal or imaginary. This equation is an incomplete quadratic equation of the form $latex ax^2+bx=0$. You can take the nature of the roots of a quadratic equation notes from the below questions to revise the concept quickly. The most common methods are by factoring, completing the square, and using the quadratic formula. Boost B2B sales Experience 20% uplift in conversion rates and 60% increase in average order value with our B2B payment solutions. Expert Answer. Then, we can form an equation with each factor and solve them. Hence the equation is a polynomial equation with the highest power as 2. The solution to the quadratic Get Assignment; Improve your math performance; Instant Expert Tutoring; Work on the task that is enjoyable to you; Clarify mathematic question; Solving Quadratic Equations by Square Root Method . 5 How do you know if a quadratic equation will be rational? TWO USA 10405 Shady Trail, #300 Dallas TX 75220. What characteristics allow plants to survive in the desert? Therefore the roots of the given equation can be found by: $\begin{array}{l}x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\end{array} $. These cookies track visitors across websites and collect information to provide customized ads. We can solve this equation by isolating the x term and taking the square root of both sides of the equation: Taking the square root of both sides, we have: The solutions to the equation are $latex x=5$ and $latex x=-5$. For what condition of a quadratic equation has two equal real root? To solve this problem, we can form equations using the information in the statement. In the more elaborately manner a quadratic equation can be defined, as one such equation in which the highest exponent of variable is squared which makes the equation something look alike as ax+bx+c=0 In the above mentioned equation the variable x is the key point, which makes it as the quadratic equation and it has no $x=4 \sqrt{3}\quad $ or $\quad x=-4 \sqrt{3}$, $y=3 \sqrt{3}\quad $ or $\quad y=-3 \sqrt{3}$. In the next example, we first isolate the quadratic term, and then make the coefficient equal to one. Note that the zeroes of the quadratic polynomial $a{x^2} + bx + c$ and the roots of the quadratic equation $a{x^2} + bx + c = 0$ are the same. The following 20 quadratic equation examples have their respective solutions using different methods. We can solve this equation by factoring. Have you? Required fields are marked *, $\begin{array}{l}3x^{2} 5x + 2 = 0\end{array} $, $\begin{array}{l}x = 1 \;\; or \;\; \frac{2}{3}\end{array} $. If $a, b, c R,$ then the roots of the quadratic equation can be real or imaginary based on the following criteria: The roots are real when $b^2 4ac0$ and the roots are imaginary when $b^2 4ac<0.$ We can classify the real roots in two parts, such as rational roots and irrational roots. Necessary cookies are absolutely essential for the website to function properly. Lets use the Square Root Property to solve the equation $x^{2}=7$. D < 0 means no real roots. has been provided alongside types of A quadratic equation has two equal roots, if? What is a discriminant in a quadratic equation? Therefore, we have: Now, we form an equation with each factor and solve: The solutions to the equation are $latex x=-2$ and $latex x=-3$. Remember when we take the square root of a fraction, we can take the square root of the numerator and denominator separately. in English & in Hindi are available as part of our courses for Class 10. We will start the solution to the next example by isolating the binomial term. Now considering that the area of a rectangle is found by multiplying the lengths of its sides, we have: Expanding and writing the equation in the form $latex ax^2+bx+c=0$, we have: Since we cant have negative lengths, we have $latex x=6$, so the lengths are 6 and 13. How do you find the nature of the roots of a quadratic equation?Ans: Since $\left({{b^2} 4ac} \right)$ determines whether the quadratic equation $a{x^2} + bx + c = 0$ has real roots or not, $\left({{b^2} 4ac} \right)$ is called the discriminant of this quadratic equation.So, a quadratic equation $a{x^2} + bx + c = 0$ has1. Consider the equation 9x 2 + 12x + 4 = 0 Comparing with the general quadratic, we notice that a = 9, b = In this chapter, we will learn three other methods to use in case a quadratic equation cannot be factored. 1 : being one more than one in number 2 : being the second used postpositively section two of the instructions two 2 of 3 pronoun plural in construction 1 : two countable individuals not specified Avoiding alpha gaming when not alpha gaming gets PCs into trouble. Solve $\left(y+\dfrac{3}{4}\right)^{2}=\dfrac{7}{16}$. Find the value of so that the quadratic equation (5 6) = 0 has two equal roots. The numbers we are looking for are -7 and 1. The mathematical representation of a Quadratic Equation is ax+bx+c = 0. The polynomial equation whose highest degree is two is called a quadratic equation. In this case the roots are equal; such roots are sometimes called double roots. The roots of the quadratic equation $a{x^2} + bx + c = 0$ are given by $x = \frac{{ b \pm \sqrt {{b^2} 4ac} }}{ {2a}}$This is the quadratic formula for finding the roots of a quadratic equation. The power of variable x is always non-negative integers. That is This will be the case in the next example. 3.8.2E: Exercises; 3.8.3: Solve Quadratic Is there only one solution to a quadratic equation? 4. amounting to two in number. When the square minus four times a C is equal to zero, roots are real, roads are real and roads are equal. To find the solutions to two quadratic equations, we need to use the Quadratic Formula. We can solve this equation using the factoring method. We have to start by writing the equation in the form $latex ax^2+bx+c=0$: Now, we see that the coefficient b in this equation is equal to -3. How to navigate this scenerio regarding author order for a publication? To solve this problem, we have to use the given information to form equations. Recall that quadratic equations are equations in which the variables have a maximum power of 2. Rewrite the radical as a fraction of square roots. Area of rectangle = Length x Width x(2x + 4) = 336 In the above formula, ( b 2-4ac) is called discriminant (d). WebShow quadratic equation has two distinct real roots. Q.4. Become a Dealer; Made 2 Fit; Dealer Login; TWO Report; Customer Support. It is a quadratic equation. Your expression following "which on comparing gives me" is not justified. $x=\pm\dfrac{\sqrt{49}\cdot {\color{red}{\sqrt 2}} }{\sqrt{2}\cdot {\color{red}{\sqrt 2}}}$, $x=\dfrac{7\sqrt 2}{2}\quad$ or $\quad x=-\dfrac{7\sqrt 2}{2}$. If you have any queries or suggestions, feel free to write them down in the comment section below. Videos Two Cliffhanger Clip: Dos More Details WebQuadratic Equation Formula: The quadratic formula to find the roots of the quadratic equation is given by: x = b b 2 4 a c 2 a Where b 2 -4ac is called the discriminant of the equation. For this, we look for two numbers, which when multiplied are equal to -7 and when added are equal to -6. This equation is an incomplete quadratic equation that does not have the bx term. A quadratic equation has two equal roots if discriminant=0, A quadratic equation has two equal roots then discriminant will equal to zero. An equation of second-degree polynomial in one variable, such as $x$ usually equated to zero, is a quadratic equation. It does not store any personal data. Watch Two | Netflix Official Site Two 2021 | Maturity Rating: TV-MA | 1h 11m | Dramas Two strangers awaken to discover their abdomens have been sewn together, and are further shocked when they learn who's behind their horrifying ordeal. Our method also works when fractions occur in the equation, we solve as any equation with fractions. This page titled 2.3.2: Solve Quadratic Equations Using the Square Root Property is shared under a CC BY license and was authored, remixed, and/or curated by OpenStax. A quadratic is a second degree polynomial of the form: ax^2+bx+c=0 where a\neq 0. Based on the discriminant value, there are three possible conditions, which defines the nature of roots as follows: two distinct real roots, if b 2 4ac > 0 Is it OK to ask the professor I am applying to for a recommendation letter? The two numbers we are looking for are 2 and 3. Add the square of half of the coefficient of x, (b/2a). 3.8.2: Solve Quadratic Equations by Completing the Square So far we have solved quadratic equations by factoring and using the Square Root Property. Can two quadratic equations have the same solution? a 1 2 + b 1 + c 1 = 0 a 1 c 1 2 + b 1 c 1 = 1. s i m i l a r l y. Quadratic equations square root - Complete The Square. Example: 3x^2-2x-1=0 (After you click the example, change the Method to 'Solve By Completing the Square'.) These roots may be real or complex. This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation. Answer: Since one solution is the reciprocal of the other, we have r1r2=1, so that a=c. The rules of the equation. For this, we look for two numbers that when multiplied are equal to 6 and when added are equal to 5. To determine the nature of the roots of any quadratic equation, we use discriminant. The roots are real but not equal. The graph of this quadratic equation touches the $x$-axis at only one point. The discriminant ${b^2} 4ac = {( 4)^2} (4 \times 2 \times 3) = 16 24 = 8 < 0$ If -5 is root of the quadratic equation 2x^2+px-15=0 and the quadratic equa. Ans: An equation is a quadratic equation in the variable $x$if it is of the form $a{x^2} + bx + c = 0$, where $a, b, c$ are real numbers, $ a 0.$. Equal or double roots. Do you need underlay for laminate flooring on concrete? Find the value of k if the quadratic equation 3x - k3 x+4=0 has equal roo, If -5 is a root of the quadratic equation 2x^2 px-15=0 and the quadratic eq. Therefore, we have: $$\left(\frac{b}{2}\right)^2=\left(\frac{-3}{2}\right)^2$$. two (tu) n., pl. How dry does a rock/metal vocal have to be during recording? The best answers are voted up and rise to the top, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, $$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$$, $$a_1\alpha^2 + b_1\alpha + c_1 = 0 \implies \frac{a_1}{c_1}\alpha^2 + \frac{b_1}{c_1}\alpha =-1$$, $$a_2\alpha^2 + b_2\alpha + c_2 = 0 \implies \frac{a_2}{c_2}\alpha^2 + \frac{b_2}{c_2}\alpha =-1$$, $$\frac{a_1}{c_1} = \frac{a_2}{c_2}, \space \frac{b_1}{c_1} = \frac{b_2}{c_2} \implies \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$$. Q.1. Two distinct real roots, if ${b^2} 4ac > 0$2. Ans: The term $\left({{b^2} 4ac} \right)$ in the quadratic formula is known as the discriminant of a quadratic equation $a{x^2} + bx + c = 0,$ $ a 0.$ The discriminant of a quadratic equation shows the nature of roots. The value of the discriminant, $D = {b^2} 4ac$ determines the nature of the Ans: The given equation is of the form $a {x^2} + bx + c = 0.$ Condition for a common root in two given quadratic equations, Condition for exactly one root being common b/w two quadratic equations. The cookies is used to store the user consent for the cookies in the category "Necessary". Use Square Root Property. For example, you could have $\frac{a_1}{c_1}=\frac{a_2}{c_2}+1$, $\frac{b_1}{c_1}=\frac{b_2}{c_2}-\alpha$. Finally, when it is not possible to solve a quadratic equation with factorization, we can use the general quadratic formula: You can learn or review the methods for solving quadratic equations by visiting our article: Solving Quadratic Equations Methods and Examples. Solving Quadratic Equations by Factoring The solution(s) to an equation are called roots. However, we can multiply it by $latex x(x-1)$ to eliminate the fractions, and we have: Now, we can factor this equation to solve it: Find the solutions to the following equation $$\frac{2x+1}{x+5}=\frac{3x-1}{x+7}$$. Comparing equation 2x^2+kx+3=0 with general quadratic equation ax^2+bx+c=0, we get, Discriminant = b^24ac=k^24(2))(3)=k^224, Putting discriminant equal to zero, we get. $r=\dfrac{6 \sqrt{5}}{5}\quad$ or $\quad r=-\dfrac{6 \sqrt{5}}{5}$, $t=\dfrac{8 \sqrt{3}}{3}\quad $ or $\quad t=-\dfrac{8 \sqrt{3}}{3}$. In a quadratic equation $a{x^2} + bx + c = 0$, if $D = {b^2} 4ac < 0$ we will not get any real roots. 3 How many solutions can 2 quadratic equations have? In a deck of cards, there are four twos one in each suit. Starring: Pablo Derqui, Marina Gatell Watch all you want. They are: Suppose if the main coefficient is not equal to one then deliberately, you have to follow a methodology in the arrangement of the factors. Transcribed image text: (a) Find the two roots y1 and y2 of the quadratic equation y2 2y +2 = 0 in rectangular, polar and exponential forms and sketch their Find the value of k? Factor the left-hand side of the equation by assuming zero on the right-hand side of the equation. What are the solutions to the equation $latex x^2-4x=0$? When B square minus four A C is greater than 20. Now solve the equation in order to determine the values of x. In the next example, we must divide both sides of the equation by the coefficient $3$ before using the Square Root Property. 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Find the discriminant of the quadratic equation $2 {x^2} 4x + 3 = 0$ and hence find the nature of its roots. A Quadratic Equation can have two roots, and they depend entirely upon the discriminant. x = -14, x = 12 Therefore, they are called zeros. We also use third-party cookies that help us analyze and understand how you use this website. Hence, our assumption was wrong and not every quadratic equation has exactly one root. WebTimes C was divided by two. While solving word problems, some common quadratic equation applications include speed problems and Geometry area problems. CBSE English Medium Class 10. Lets review how we used factoring to solve the quadratic equation $x^{2}=9$. (i) 2x2 + kx + 3 = 0 2x2 + kx + 3 = 0 Comparing equation with ax2 + bx + c = 0 a = 2, b = k, c = 3 Since the equation has 2 equal roots, D = 0 b2 4ac = 0 Putting values k2 The number of roots of a polynomial equation is equal to its degree. Hence, a quadratic equation has 2 roots. Let and be the roots of the general form of the quadratic equation :ax 2 + bx + c = 0. For exmaple, if the only solution to to a quadratic equation is 20, then the equation would be: which gives . We have seen that some quadratic equations can be solved by factoring. We can solve this equation by solving for x and taking the square root of both sides: The solutions of the equation are $latex x=4$ and $latex x=-4$. Can two quadratic equations have same roots? But even if both the quadratic equations have only one common root say then at x = . n. 1. a cardinal number, 1 plus 1. Leading AI Powered Learning Solution Provider, Fixing Students Behaviour With Data Analytics, Leveraging Intelligence To Deliver Results, Exciting AI Platform, Personalizing Education, Disruptor Award For Maximum Business Impact, Reduce Silly Mistakes; Take Free Mock Tests related to Quadratic Equations, Nature of Roots of a Quadratic Equation: Formula, Examples. Legal. Letter of recommendation contains wrong name of journal, how will this hurt my application? Two distinct real roots 2. But what happens when we have an equation like $x^{2}=7$? On the other hand, we can say $x$ has two equal solutions. More examples. We can classify the roots of the quadratic equations into three types using the concept of the discriminant. That is, ( ( ( 5 k) 2 4 ( 1) ( k + 2) > 0). The solutions are $latex x=7.46$ and $latex x=0.54$. Idioms: 1. in two, into two separate parts, as halves. Ans: The form $a{x^2} + bx + c = 0,$ $ a 0$ is called the standard form of a quadratic equation. How can you tell if it is a quadratic equation? Consider, ${x^2} 4x + 1 = 0.$The discriminant $D = {b^2} 4ac = {( 4)^2} 4 \times 1 \times 1 \Rightarrow 16 4 = 12 > 0$So, the roots of the equation are real and distinct as $D > 0.$Consider, ${x^2} + 6x + 9 = 0$The discriminant ${b^2} 4ac = {(6)^2} (4 \times 1 \times 9) = 36 36 = 0$So, the roots of the equation are real and equal as $D = 0.$Consider, $2{x^2} + x + 4 = 0$, has two complex roots as $D = {b^2} 4ac \Rightarrow {(1)^2} 4 \times 2 \times 4 = 31$ that is less than zero. Comparing equation 2x^2+kx+3=0 with general quadratic The discriminant can be evaluated to determine the character of the solutions of a quadratic equation, thus: if , then the quadratic has two distinct real number roots. In order to use the Square Root Property, the coefficient of the variable term must equal one. Try working with these equations which have only one common root. $x= 6 \sqrt{2} i\quad$ or $\quad x=- 6 \sqrt{2} i$. Divide both sides by the coefficient $4$. Example: Find the width of a rectangle of area 336 cm2 if its length is equal to the 4 more than twice its width. Find the roots of the equation $latex 4x^2+5=2x^2+20$. $x=\dfrac{1}{2}+\dfrac{\sqrt{5}}{2}\quad$ or $\quad x=\dfrac{1}{2}-\dfrac{\sqrt{5}}{2}$. If $latex X=5$, we have $latex Y=17-5=12$. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. The Square Root Property states If $x^{2}=k$, What will happen if $k<0$? Solve a quadratic equation using the square root property. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. Remember to write the $\pm$ symbol or list the solutions. All while we take on the risk. Discriminant can be represented by $D.$. This is an incomplete quadratic equation that does not have the c term. But opting out of some of these cookies may affect your browsing experience. Use the Square Root Property on the binomial. Some of the most important methods are methods for incomplete quadratic equations, the factoring method, the method of completing the square, and the quadratic formula. In a quadratic equation $a{x^2} + bx + c = 0,$ we get two equal real roots if $D = {b^2} 4ac = 0.$ In the graphical representation, we can see that the graph of the quadratic equation having equal roots touches the x-axis at only one point. Statement-II : If p+iq is one root of a quadratic equation with real coefficients, then piq will be the other root ; p,qR,i=1 . Q.7. The solution for this equation is the values of x, which are also called zeros. $latex \sqrt{-184}$ is not a real number, so the equation has no real roots. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Putting the values of x in the LHS of the given quadratic equation, $\begin{array}{l}y=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\end{array} $, $\begin{array}{l}y=\frac{-(2) \pm \sqrt{(2)^{2}-4(1)(-2)}}{2(1)}\end{array} $, $\begin{array}{l}y=\frac{-2 \pm \sqrt{4+8}}{2}\end{array} $, $\begin{array}{l}y=\frac{-2 \pm \sqrt{12}}{2}\end{array} $. WebQuadratic equations square root - Complete The Square. $x=\sqrt{k} \quad$ or $\quad x=-\sqrt{k} \quad$. These two distinct points are known as zeros or roots. Step 1. Example: 3x^2-2x-1=0 (After you click the example, change the Method to 'Solve By Completing the Square'.) The mathematical representation of a Quadratic Equation is ax+bx+c = 0. Add the square of half of the coefficient of x, (b/2a)2, on both the sides, i.e., 1/16. Check the solutions in order to detect errors. We can solve incomplete quadratic equations of the form $latex ax^2+c=0$ by completely isolating x. { "2.3.2E:_Exercises" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "2.3.01:_Solving_Quadratic_Equations_by_Factoring" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3.02:_Solve_Quadratic_Equations_Using_the_Square_Root_Property" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3.03:_Solve_Quadratic_Equations_by_Completing_the_Square" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3.04:_Solve_Quadratic_Equations_Using_the_Quadratic_Formula" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3.05:_Solve_Applications_of_Quadratic_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3.06:_Chapter_9_Review_Exercises" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3.07:_Graph_Quadratic_Equations_Using_Properties_and_Applications" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.3.08:_Graph_Quadratic_Equations_Using_Transformations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "2.01:_Introduction_to_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.02:_Linear_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.03:_Quadratic_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.04:_Solve_Radical_Equations_with_Applications" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.05:_Polynomial_Equations_with_Applications" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "2.06:_Solve_Rational_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 2.3.2: Solve Quadratic Equations Using the Square Root Property, [ "article:topic", "authorname:openstax", "license:ccby", "showtoc:no", "source[1]-math-5173", "source[2]-math-5173", "source[21]-math-67011", "source[22]-math-67011" ], https://math.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fmath.libretexts.org%2FCourses%2FCity_University_of_New_York%2FCollege_Algebra_and_Trigonometry-_Expressions_Equations_and_Graphs%2F02%253A_II-_Equations_with_One_Unknown%2F2.03%253A_Quadratic_Equations%2F2.3.02%253A_Solve_Quadratic_Equations_Using_the_Square_Root_Property, $ \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}$ $ \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} $$\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$ $\newcommand{\id}{\mathrm{id}}$ $ \newcommand{\Span}{\mathrm{span}}$ $ \newcommand{\kernel}{\mathrm{null}\,}$ $ \newcommand{\range}{\mathrm{range}\,}$ $ \newcommand{\RealPart}{\mathrm{Re}}$ $ \newcommand{\ImaginaryPart}{\mathrm{Im}}$ $ \newcommand{\Argument}{\mathrm{Arg}}$ $ \newcommand{\norm}[1]{\| #1 \|}$ $ \newcommand{\inner}[2]{\langle #1, #2 \rangle}$ $ \newcommand{\Span}{\mathrm{span}}$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$, Solve a Quadratic Equation Using the Square Root Property, 2.3.1: Solving Quadratic Equations by Factoring, Solve Quadratic Equations of the Form $ax^{2}=k$ using the Square Root Property, Solve Quadratic Equation of the Form $a(x-h)^{2}=k$ Using the Square Root Property, status page at https://status.libretexts.org, $x=\sqrt 7\quad$ or $\quad x=-\sqrt 7$. 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