Quadratic Equations and Linear Inequalities — Formula Sheet

A quadratic equation has the standard form ax² + bx + c = 0, where a ≠ 0. Here 'a' is the leading coefficient, 'b' is the middle coefficient, and 'c' is the constant term.

The discriminant D = b² - 4ac determines the NATURE of roots BEFORE actually computing them.

If D > 0

two distinct real roots. If D = 0: two equal real roots (each equal to -b/2a). If D < 0: two complex conjugate roots.

For the quadratic equation ax² + bx + c = 0 with roots α and β: Sum of roots = α + β = -b/a, Product of roots = αβ = c/a.

To form a new quadratic equation with given roots p and q

x² - (p + q)x + pq = 0.

A universal formula to find roots of any quadratic equation ax² + bx + c = 0: x = (-b ± √D) / (2a), where D = b² - 4ac is the discriminant.