Search results
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 in its standard form is represented as: ax 2 + bx + c = 0, where a, b and c are real numbers such that a ≠ 0 and x is a variable. The number of roots of a polynomial equation is equal to its degree. So, a quadratic equation has two roots. Some methods for finding the roots are: Factorization method; Quadratic Formula ...
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.
A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation [3] where r and s are the solutions for x.
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.
