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The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
We shall learn how to find the roots of quadratic equations algebraically and using the quadratic formula. The general form of a quadratic equation is ax 2 + bx + c = 0, where x is the unknown and a, b and c are known quantities such that a ≠ 0.
May 28, 2024 · Roots of Quadratic Equation. The roots of a quadratic equation, which is typically written as ax 2 + bx + c = 0 where a, b, and c are constants and a ≠ 0. Roots of a Quadratic Equation are the values of the variable let’s say x for which the equation gets satisfied.
A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real. Factoring by inspection. It may be possible to express a quadratic equation ax2 + bx + c = 0 as a product (px + q) (rx + s) = 0.
The roots of a quadratic equation are the two values of x, which are obtained by solving the quadratic equation. These roots of the quadratic equation are also called the zeros of the equation. For example, the roots of the equation x 2 - 3x - 4 = 0 are x = -1 and x = 4 because each of them satisfies the equation. i.e.,
Quadratic Equation in Standard Form: ax 2 + bx + c = 0; Quadratic Equations can be factored; Quadratic Formula: x = −b ± √(b 2 − 4ac) 2a; When the Discriminant (b 2 −4ac) is: positive, there are 2 real solutions; zero, there is one real solution; negative, there are 2 complex solutions
Dec 13, 2023 · A highly dependable method for solving quadratic equations is the quadratic formula, based on the coefficients and the constant term in the equation. See Example. The discriminant is used to indicate the nature of the roots that the quadratic equation will yield: real or complex, rational or irrational, and how many of each. See Example.
Then the formula will help you find the roots of a quadratic equation, i.e. the values of x where this equation is solved. The quadratic formula. x = − b ± b 2 − 4 a c 2 a. It may look a little scary, but you’ll get used to it quickly! Practice using the formula now. Worked example.
Google Classroom. Learn how to solve quadratic equations like x^2=36 or (x-2)^2=49. What you should be familiar with before taking this lesson. Square roots. Special products of binomials. What you will learn in this lesson.
Roots of a Quadratic Equation. The number of roots of a polynomial equation is equal to its degree. Hence, a quadratic equation has 2 roots. Let α and β be the roots of the general form of the quadratic equation :ax 2 + bx + c = 0. We can write: α = (-b-√b 2 -4ac)/2a and β = (-b+√b 2 -4ac)/2a. Here a, b, and c are real and rational.
