Quadratic Equations — Formula Sheet

ax^2 + bx + c = 0

p(x) = 0, where p(x) is a polynomial of degree 2

Factorisation: split middle term using p + q = b and p × q = a × c

Quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Completing the square: [x + b/(2a)]^2 = (b^2 - 4ac) / (4a^2)

Discriminant: D = b^2 - 4ac

Sum of roots: -b/a

x^2 - 45x + 324 = 0

x^2 - 36x + 308 = 0

x^2 - 9 = 0

The quadratic formula gives the roots directly when b^2 - 4ac ≥ 0.

A real number α is a root if substituting x = α makes the equation true, so aα^2 + bα + c = 0.