Question

Solve the following equation; give irrational answers in terms of surds.
$x^4-5x^2-6=0$

Answer 1

$x^4-5x^2-6=0$

$x^4-6x^2+x^2-6=0$

$x^2(x^2-6)+1(x^2-6)=0$

$(x^2+1)(x^2-6)=0$

Now, $x^2+1=0x^2=-1x=\pm i(i^2=-1)$ Or $x^2-6=0x=\pm \sqrt{6}$

$x=i,-i,+\sqrt{6},-\sqrt{6}$