Question

What are the solutions to the equation x^4+3x^2+2=0?

Answer 1

i, -i , 2i, -2i

Explanation:

We can factor this as follows:-

x^4 + 3x^2 + 2 = 0

(x^2 + 1)(x^2 + 2) = 0

By the zero product postulate:-

x^2 + 1 = 0 or x^2 + 2 = 0

x^2 + 1 = 0

x = +/- √-1 = i , -i

x^2 + 2 = 0

x = +/- √-2 = 2 √-1 , -2√-1 = 2i; -2i.