Roots and the zero-product principle

A root makes a quadratic equation true. If \(AB=0\), at least one factor is zero. First put the equation in the form \(ax^2+bx+c=0\), then factorise and set each factor equal to zero.

Example

\(\begin{aligned}x^2+x&=20\\x^2+x-20&=0\\(x+5)(x-4)&=0\\x&=-5\quad\text{or}\quad x=4.\end{aligned}\)

Both satisfy the original equation: \(25-5=20\) and \(16+4=20\).

Do not divide away a factor containing the unknown. For \(x(x-3)=0\), the roots are \(0\) and \(3\); dividing by \(x\) would lose \(0\). The zero-product principle requires a product equal to zero.