What are the solutions of the equation x⁴ - 5x² - 36 = 0? Use factoring to solve.

Solution:

The equation given is

x⁴ - 5x² - 36 = 0

By factoring the left side we get

(x² - 9) (x² + 4) = 0

Factoring using the algebraic identity a² - b² = (a + b) (a - b)

(x - 3) (x + 3) (x² + 4) = 0

By equating each factor to 0

x - 3 = 0 and x + 3 = 0 and x² + 4 = 0

So we get

x = 3 and x = -3 and x² = -4

x = 3 and x = -3 and x = 2i or -2i

Therefore, solutions of the equation are 3, -3, 2i and -2i.

What are the solutions of the equation x⁴ - 5x² - 36 = 0? Use factoring to solve.

Summary:

The solutions of the equation x⁴ - 5x² - 36 = 0 are 3, -3, 2i and -2i.