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Quadratic Equation by Completing the Square Part-2 (Deducted from CBSE 2021-22 examination) Video Lecture - Class 10

Q: 2. How do you complete the square to solve a quadratic equation?

Ans. To complete the square, follow these steps:1. Write the quadratic equation in the form: $ax^2 + bx + c = 0$.2. Divide the equation by the coefficient of $x^2$ if necessary to make $a = 1$.3. Move the constant term ($c$) to the right side of the equation.4. Take half of the coefficient of $x$ ($b$), square it, and add it to both sides of the equation.5. Rewrite the left side of the equation as a perfect square trinomial.6. Take the square root of both sides of the equation.7. Solve for $x$ by isolating it on one side of the equation.

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FAQs on Quadratic Equation by Completing the Square Part-2 (Deducted from CBSE 2021-22 examination) Video Lecture - Class 10

1. What is completing the square method in solving quadratic equations?

Ans. Completing the square is a method used to solve quadratic equations that cannot be easily factored. It involves manipulating the equation to create a perfect square trinomial, which can then be easily solved by taking the square root of both sides.

2. How do you complete the square to solve a quadratic equation?

Ans. To complete the square, follow these steps: 1. Write the quadratic equation in the form: $ax^2 + bx + c = 0$. 2. Divide the equation by the coefficient of $x^2$ if necessary to make $a = 1$. 3. Move the constant term ($c$) to the right side of the equation. 4. Take half of the coefficient of $x$ ($b$), square it, and add it to both sides of the equation. 5. Rewrite the left side of the equation as a perfect square trinomial. 6. Take the square root of both sides of the equation. 7. Solve for $x$ by isolating it on one side of the equation.

3. Can all quadratic equations be solved using completing the square method?

Ans. Yes, completing the square method can be used to solve any quadratic equation, even if it cannot be easily factored. However, it can be a more time-consuming process compared to factoring or using the quadratic formula.

4. Are there any shortcuts or alternative methods to solving quadratic equations?

Ans. Yes, besides completing the square, there are two other commonly used methods to solve quadratic equations. One is factoring, where the quadratic equation is factored into two binomials and each binomial is set equal to zero. The other method is using the quadratic formula, which directly gives the solutions of the quadratic equation without the need for factoring or completing the square.

5. Is completing the square method taught in Class 10 CBSE curriculum?

Ans. Yes, completing the square method is a part of the Class 10 CBSE curriculum for quadratic equations. Students are taught how to manipulate equations to create perfect square trinomials and use them to solve quadratic equations. It is an important skill that helps in understanding the concepts of quadratic equations and their solutions.

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