You have the following function:
f(x) = x⁴ - 5x² - 36
In order to find the roots of the given function, rewrite it as follow:
f(x) = (x²)² - 5(x²) - 36
you can write the previous expression as the product of two factors:
f(x) = (x² - )(x² + )
where in the blank space, you put two numbers that multiplied between them result in 36 and subtracted result in 5. Such numbers are 9 and 4.
Then, you have:
f(x) = (x² - 9)(x² + 4)
next, consider that each factor is equal to zero:
x² - 9 = 0
x = 9
x = ±3
x² + 4 = 0
x = -4
x = ±2i
Hence, the roots of the given function are 3, -3, 2i, -2i.