Question

How do you solve the modulus of a quadratic equation?

Answer 1

Let us take an example to solve the modulus of a quadratic equation:

$|x^2–6|=-x+6$

Step 1. When $|x^2–6|\ge 0$,

then, $x^2–6=-x+6$

$\Rightarrow$ $x^2+x–12=0$

$\Rightarrow$ $x^2–3x+4x–12=0$

$\Rightarrow$$x(x–3)+4(x–3)=0$

$\Rightarrow$ $(x–3)(x+4)=0$

$\therefore$$x=3orx=-4$

Step 2. When $|x^2–6|<0$,

then, $-(x^2–6)=-x+6$

$\Rightarrow$ $x^2–x=0$

$\Rightarrow$ $x(x–1)=0$

$\therefore$$x=0orx=1$

Hence, there are four solutions for the assumed modulus quadratic equation, they are $\mathbf{0}\mathbf{,}\mathbf{}\mathbf{1}\mathbf{,}\mathbf{}\mathbf{2}\mathbf{,}\mathbf{}\mathbf{-}\mathbf{4}$.