find all the roots of x^4-8x^2+5.

Answer 1

Treat x^2 as a new variable, u. Then use the quadratic equation to solve for u.

u^2 -8u + 5 = 0

u = (8 +/-sqrt44)/2 = 7.3166 and 0.6839

The square roots of the two u values you get will be the four values of x that are roots of the original equation.