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Quadratic Equation by Completing the Square (Part-1) Video Lecture - Class 10
FAQs on Quadratic Equation by Completing the Square (Part-1) Video Lecture - Class 10
| 1. What is the quadratic equation and how is it solved by completing the square? |  |
Ans. A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. To solve a quadratic equation by completing the square, follow these steps:
1. Arrange the equation in the form ax^2 + bx = -c.
2. Add (b/2a)^2 to both sides of the equation to make the left side a perfect square trinomial.
3. Rewrite the left side of the equation as (x + b/2a)^2.
4. Take the square root of both sides of the equation.
5. Solve for x by isolating it on one side of the equation.
| 2. Why is completing the square method used to solve quadratic equations? | |
Ans. The completing the square method is used to solve quadratic equations because it provides a systematic and reliable approach to finding the roots of a quadratic equation. This method is particularly useful when the quadratic equation cannot be easily factored or when the quadratic coefficient (a) is not equal to 1. By converting the quadratic equation into a perfect square trinomial, the solutions can be easily obtained by taking the square root and solving for x.
| 3. Can all quadratic equations be solved using the completing the square method? | |
Ans. Yes, all quadratic equations can be solved using the completing the square method. However, it may not always be the most efficient method, especially when the quadratic equation can be easily factored or when the coefficients are simple. In such cases, factoring or using the quadratic formula may be more suitable. Nevertheless, completing the square method is a reliable method that can always be used to find the solutions of a quadratic equation.
| 4. Are there any limitations or difficulties when using the completing the square method? | |
Ans. While the completing the square method is a powerful tool for solving quadratic equations, it does have some limitations and difficulties. One limitation is that the method can be time-consuming and involve several steps, especially when the coefficients are large or involve fractions. Additionally, the method requires careful algebraic manipulation and understanding of square roots. It may be challenging for individuals who are not familiar with these concepts or who struggle with algebraic manipulations.
| 5. Can the completing the square method be used to solve equations other than quadratic equations? | |
Ans. The completing the square method is primarily used to solve quadratic equations. However, the concept of completing the square can be extended to solve other types of equations as well. It is commonly used in calculus and higher-level mathematics to solve problems involving complex numbers or quadratic forms. In these cases, completing the square can help in simplifying the equations and finding their solutions.
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