A quadratic equation in one variable (say x) is a polynomial equation in which the highest power of the variable is two.
An equation of the form ax2 + bx + c = 0, where a, b, c are real numbers and a ≠ 0 represents standard form of a quadratic equation.
A number α is said to be the root of a quadratic equation ax2 + bx + c = 0, if
aα2 + bα +c = 0. Any quadratic equation can have at most two roots.
Following three methods are used to solve a quadratic equation:
In this method, the given quadratic equation is factorized into a product of two linear factors, each of which are then equated to zero to find the roots of the equation.
2) Completing the square
• Write LHS as the perfect square of a binomial expression and simplify RHS.
• Take the square root of both sides.
• Obtain the roots by shifting the constant term on RHS.
3) Quadratic Formula
The roots of the quadratic equation ax2 + bx + c = 0, a ≠ 0 can be found by using quadratic formula:
b2 – 4ac is the discriminant of the quadratic equation ax2 + bx + c = 0, a ≠ 0. It is denoted by D.
D > 0 implies that the equation has two distinct real roots.
D = 0 implies that the equation has two equal real roots.
D < 0 implies that the equation has non-real roots.