Quadratic Equations

The general form ax² + bx

The general form ax² + bx + c = 0, where 'a' is the coefficient of x² (a ≠ 0), 'b' is the coefficient of x, and 'c' is the constant term. Example: x²

Breaking down the quadratic expression into

Breaking down the quadratic expression into two linear factors. If x² - 4x - 5 = (x - 5)(x + 1), then (x - 5)(x + 1) = 0 gives roots x = 5 or x = -1.

Converting the quadratic expression into

Converting the quadratic expression into a perfect square form. For x² + 10x + 2 = 0, we write it as (x + 5)² - 23 = 0, leading to x = -5 ± √23.

The universal solution x = (

The universal solution x = (-b ± √(b² - 4ac))/2a works for any quadratic equation. It provides both roots directly by substituting the values of a, b,

Determines the nature of roots

Determines the nature of roots: If Δ > 0, roots are real and unequal; if Δ = 0, roots are real and equal; if Δ < 0, roots are not real.