Question

Hi guys. I’m not sure how to answer this so I was wondering if you guys could help me.

Question: what are the roots of the following polynomial x cubed - 9x?

How would I do this correctly? Please do a step by step answer.
Thanks!

Answer 1

x = 0, x = ± 3

Explanation:

To find the roots equate the polynomial to zero, that is solve

x³ - 9x = 0 ← factor out x from both terms

x(x² - 9) = 0 ← factor difference of squares

x(x - 3)(x + 3) = 0

equate each factor to zero and solve for x

x = 0

x - 3 = 0 ⇒ x = 3

x + 3 = 0 ⇒ x = - 3

roots are x = 0, x = ± 3