Question

SOLVE x^4 − 15x^2 − 16 = 0
What are the roots of the equation?

Answer 1

roots : 4, -4, i, -i

Explanation:

This gets a bit tricky.

We have to substitude x^2 as u in this problem.

Now to rewrite x^4 − 15x^2 − 16 = 0 with u, we get

u^2 - 15u - 16 = 0

( u - 16) (u + 1)

U = 16

U = -1

This is not the end of the problem.

Now we have to substitute x^2 back to u.

x^2 = 16 --> we get the roots 4 and -4

x^2 = -1 --> we get the roots i and -i

tadah!