Question

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

Answer 1

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

Step-by-step explanation:

To solve the equation x4 - 5x2 - 36 = 0 using factoring, we can first factor it as (x2 - 9)(x2 + 4) = 0. This can be further factored as (x - 3)(x + 3)(x2 + 4) = 0. Since the quadratic x2 + 4 does not have real solutions, the solutions of the equation are x = 3 and x = -3.

Answer 2

x^4 - 5x^2 - 36 = 0
(x^2 - 9)(x^2 + 4) = 0 - factor the left side
(x + 3)(x - 3)(x^2 + 4) = 0 - factor (x^2 - 9 as difference of squares)
x + 3 = 0 x - 3 = 0 x^2 + 4 = 0 Set each factor to 0 if any 0 the left side 0
x = -3 x = 3 x^2 = -4
x = 2i or -2i
The roots are 3, -3, 2i, -2i (Don't know if you need the imaginary roots but I gave you them anyway)