Quadratic Equations

A quadratic equation is an equation

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0. The highest degree of the variable x is 2.

A real number α is called

A real number α is called a root of the quadratic equation ax² + bx + c = 0 if aα² + bα + c = 0. The roots are also called solutions or zeros of the e

This method involves expressing the quadratic

This method involves expressing the quadratic polynomial ax² + bx + c as a product of two linear factors. If ax² + bx + c = (px + q)(rx + s), then the

For any quadratic equation ax² +

For any quadratic equation ax² + bx + c = 0, the roots are given by x = (-b ± √(b² - 4ac))/2a, provided b² - 4ac ≥ 0. This formula works for all quadr

The discriminant Δ = b²

The discriminant Δ = b² - 4ac determines the nature of roots: (i) If Δ > 0: two distinct real roots, (ii) If Δ = 0: two equal real roots, (iii) If Δ <