Question

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

Answer 1

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