Question

What are the solutions of the equation x4 – 5x2 – 36 = 0? Use factoring to solve.
x = ±2 and x = ±3
x = ±2i and x = ±3
x = ±2 and x = ±3i
x = ±2i and x = ±3i

Answer 1

Let y = x^2. Then y^2 − 5y − 36 = 0 factors as (y − 9)(y + 4) = 0, so y = 9 or y = −4.

Thus x^2 = 9 ⇒ x = ±3, and x^2 = −4 ⇒ x = ±2i.

Equivalently, x^4 − 5x^2 − 36 = (x^2 − 9)(x^2 + 4) = (x − 3)(x + 3)(x − 2i)(x + 2i).

Answer: x = ±2i and x = ±3.