Question

What are the solutions of the equation x^4+95x^2-500=0

Answer 1

x = ± 10i or x = ±√5

consider the factors of - 500 which sum to + 95

These are + 100 and - 5

`x^(4)` + 95x² - 500 = (x² + 100)(x² - 5) = 0

equate each factor to zero and solve for x

x² + 100 = 0 ⇒ x² = - 100 has no real solutions but has complex roots

x = ± 10i

x² - 5 = 0 ⇒ x² = 5 ⇒ x = ±√5