Quadratic Equations and Their Solutions from "summary" of NCERT Class 10 Mathematics Solutions by JagranJosh
A quadratic equation is a type of equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The highest power of the variable x in a quadratic equation is 2, which is why it is called a quadratic equation. Solving a quadratic equation involves finding the values of the variable x that satisfy the equation. These values are known as the solutions of the quadratic equation. There are different methods to solve quadratic equations, such as factorization, completing the square, and using the quadratic formula. One of the most commonly used methods to solve quadratic equations is the quadratic formula, which states that the solutions of a quadratic equation ax^2 + bx + c = 0 can be found using the formula x = (-b ± √(b^2 - 4ac)) / 2a. This formula can be used for any quadratic equation, regardless of the values of a, b, and c. Another method to solve quadratic equations is by factorization, which involves expressing the quadratic equation as a product of two linear factors. By setting each factor equal to zero, we can find the solutions of the quadratic equation. Completing the square is another method to solve quadratic equations, which involves rewriting the quadratic equation in the form (x - p)^2 = q. By taking the square root of both sides, we can find the solutions of the quadratic equation. Understanding how to solve quadratic equations is important in mathematics, as they have many applications in various fields, such as physics, engineering, and economics. By mastering the methods to solve quadratic equations, one can enhance their problem-solving skills and analytical thinking.
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