Question

What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.
x = plus-or-minus StartRoot 5 EndRoot and x = ±10
x = plus-or-minus i StartRoot 5 EndRoot and x = ±10i
x = plus-or-minus StartRoot 5 EndRoot and x = ±10i
x = plus-or-minus i StartRoot 5 EndRoot and x = ±10

Answer 1

Let y = x^2. Then y^2 + 95y - 500 = 0 factors as (y - 5)(y + 100) = 0, so y = 5 or y = -100. Thus

x^2 = 5 → x = ±√5,
x^2 = -100 → x = ±10i.

So the solutions are x = ±√5 and x = ±10i (the third choice).