Solving Cubic Equations (Grade 12 NSC Matric Mathematics): Flashcards

$ax^3 + bx^2 + cx + d = 0$ where $a \neq 0$

Equation would reduce to quadratic or lower degree

$(x - a)$ is a factor of the polynomial

Use factor theorem to find one factor

Simple integers like $\pm 1$, $\pm 2$, $\pm 3$

Divide cubic by this factor to get quadratic factor

When quadratic factor cannot be factorised by inspection

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

3 real solutions

Only 1 real solution (from factor theorem)