Quadratic Equations

A quadratic equation is written as

A quadratic equation is written as ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0. The coefficient 'a' cannot be zero because then it woul

A root (or solution) of ax²

A root (or solution) of ax² + bx + c = 0 is a value of x that makes the equation true. If α is a root, then aα² + bα + c = 0. A quadratic equation can

Step

Step-by-step process: (1) Write equation in standard form, (2) Factor the quadratic expression, (3) Use zero product property: if AB = 0, then A = 0 o

For ax² + bx + c

For ax² + bx + c = 0, roots are given by x = (-b ± √(b²-4ac))/2a. This formula works for all quadratic equations. Example: For 2x² - 7x + 3 = 0, x = (

Discriminant D = b²

Discriminant D = b² - 4ac determines root nature: (1) If D > 0: two distinct real roots, (2) If D = 0: two equal real roots, (3) If D < 0: no real roo