Question

What are the types of roots of the equation below?

x^4 - 81 = 0​

Answer 1

x^4 - 81 = 0

(x² - 9)(x² + 9) = 0

Notice that the first of these is itself a difference of two squares:

(x - 3)(x + 3)(x² + 9) = 0

So the solutions are x = 3, x = -3, x = 3i, x = -3i