Quadratic Equations

ax^2 + bx + c = 0, a ≠ 0

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Factorisation method: If (p)(q) = 0, then p = 0 or q = 0

Quadratic formula: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Repeated root case: x = -\frac{b}{2a}

Discriminant: b^2 - 4ac

If b^2 - 4ac > 0, two distinct real roots

If b^2 - 4ac = 0, two equal real roots

If b^2 - 4ac < 0, no real roots

Area of rectangle = length × breadth

Pythagoras theorem: AP^2 + BP^2 = AB^2