Quadratic Equations

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: 1) Factorisation 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.

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