Answer
$\left\{-\dfrac{\sqrt{6}}{3},-\dfrac{1}{2},\dfrac{1}{2},\dfrac{\sqrt{6}}{3}\right\}$.
Work Step by Step
Using factoring of trinomials, the given equation, $
12x^4-11x^2+2=0
,$ is equivalent to
\begin{align*}
(4x^2-1)(3x^2-2)=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable, then
\begin{array}{l|r}
4x^2-1=0 & 3x^2-2=0
\\
4x^2=1 & 3x^2=2
\\\\
x^2=\dfrac{1}{4} & x^2=\dfrac{2}{3}
\end{array}
Taking the square root of both sides (Square Root Property), the equations above are equivalent to
\begin{array}{l|r}
x=\pm\sqrt{\dfrac{1}{4}} & x=\pm\sqrt{\dfrac{2}{3}}
\\\\
x=\pm\dfrac{1}{2} & x=\pm\sqrt{\dfrac{2}{3}\cdot\dfrac{3}{3}}
\\\\
& x=\pm\sqrt{\dfrac{1}{9}\cdot6}
\\\\
& x=\pm\dfrac{1}{3}\sqrt{6}
\\\\
& x=\pm\dfrac{\sqrt{6}}{3}
\end{array}
Hence, the solution set of the equation $
12x^4-11x^2+2=0
$ is $\left\{-\dfrac{\sqrt{6}}{3},-\dfrac{1}{2},\dfrac{1}{2},\dfrac{\sqrt{6}}{3}\right\}$.
