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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.
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.
May 28, 2024 · Roots of Quadratic Equations are also called Zeros of a Quadratic Equation or Solutions of a Quadratic Equation. Quadratic equations are mathematical expressions of the form ax 2 + bx + c = 0, where a, b, and c are constants, and x represents the variable.
The formula to find the roots of the quadratic equation is x = [-b ± √(b 2 - 4ac)]/2a. The sum of the roots of a quadratic equation is α + β = -b/a. The product of the Root of the quadratic equation is αβ = c/a. The quadratic equation whose roots are α, β, is x 2 - (α + β)x + αβ = 0.
6 days ago · A quadratic equation has two roots which may be unequal real numbers or equal real numbers, or numbers which are not real. If a quadratic equation has two real equal roots α, we say the equation has only one real solution. Example: Let 3x 2 2 + x - 2 = 0 be a quadratic equation. Clearly, 3 ∙ (-1) 2 2 + (-1) - 2 = 0.
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.
