Find the roots for f (x) = x4 + 21x2 - 100.

We will use the substitution:

t = x²;

t² + 21 x - 100 = 0

t² + 25 t - 4 t - 100 = 0

t (t + 25) - 4 (t + 25) = 0

(t + 25) (t - 4) = 0

t 1 = - 25, t 2 = 4

x = √t

Answer:

The roots are:

x 1 = 5 i

x 2 = - 5 i

x 3 = - 2

x 4 = 2