The question is:
[tex]\begin{gathered} 5x^4-16x^2=16 \\ 5x^4-16x^2-16=0 \end{gathered}[/tex]
Factor as follows:
[tex]\begin{gathered} 5x^4-16x^2-16=0 \\ 5x^4-20x^2+4x^2-16=0 \\ 5x^2(x^2-4)+4(x^2-4)=0 \\ (5x^2+4)(x^2-4)=0 \\ (5x^2+4)(x-2)(x+2)=0 \end{gathered}[/tex]
So the values of x are:
[tex]\begin{gathered} x^2=-\frac{4}{5},x=2,-2 \\ x=\pm\frac{2}{\sqrt[]{5}}i,x=2,x=-2 \end{gathered}[/tex]
Hence there are two imaginary and two real roots for the equation.
The real roots are x=2 and x=-2.
Imaginary roots are:
[tex]x=\frac{2}{\sqrt[]{5}}i,x=-\frac{2}{\sqrt[]{5}}i[/tex]
