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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.
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.
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.
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.
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
The formula for a quadratic equation is used to find the roots of the equation. Since quadratics have a degree equal to two, therefore there will be two solutions for the equation. Suppose ax² + bx + c = 0 is the quadratic equation, then the formula to find the roots of this equation will be: x = [-b±√ (b2-4ac)]/2a.
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.
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.
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.,
