Quadratic Equations — Chapter Summary

The standard form is ax^2 +

The standard form is ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Any equation that can be simplified into this form is a quadrati

A real number α is

A real number α is a root of ax^2 + bx + c = 0 if aα^2 + bα + c = 0. The zeroes of a quadratic polynomial and the roots of the corresponding quadratic

Quadratic equations are solved by factorisation

Quadratic equations are solved by factorisation, completing the square, and the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a.

The quadratic expression is split into

The quadratic expression is split into factors, and each factor is set equal to zero. For example, 2x^2 - 5x + 3 = 0 becomes (2x - 3)(x - 1) = 0, so t

For ax^2 + bx + c

For ax^2 + bx + c = 0, the roots are x = (-b ± √(b^2 - 4ac)) / 2a. It gives the roots directly from the coefficients.