Question

what are the solutions of the equation (x^4 - 5x^2 - 36 = 0)? use factoring to solve.

(x = \pm 2) and (x = \pm 3)
(x = \pm 2i) and (x = \pm 3)
(x = \pm 2) and (x = \pm 3i)
(x = \pm 2i) and (x = \pm 3i)

Explanation:

Substitute to rewrite in quadratic form

$$ \text{Let } u = x^2. \text{ The equation } x^4 - 5x^2 - 36 = 0 \text{ becomes } u^2 - 5u - 36 = 0. $$

Factor the quadratic equation

$$ (u - 9)(u + 4) = 0 \implies u = 9 \text{ or } u = -4. $$

Solve for x by substituting back

$$
LATEXBLOCK0
$$

Answer:

• (A) \(x = \pm 2\) and \(x = \pm 3\)
• (B) \(x = \pm 2i\) and \(x = \pm 3\) (Correct answer)
• (C) \(x = \pm 2\) and \(x = \pm 3i\)
• (D) \(x = \pm 2i\) and \(x = \pm 3i\)