A cubic equation has factors of (x + 2) (x2 + 7x + 10). Determine ALL of the real roots. Which one is a double root?

A) x = 2 and x = 5; 2

B) x = - 2 and x = 5; - 2

C) x = 2 and x = - 5; - 5

D) x = - 2 and x = - 5; - 2

D

Step-by-step explanation:

To determine the roots equate the factors to zero, that is

(x + 2) (x² + 7x + 10) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x² + 7x + 10 = 0

(x + 2) (x + 5) = 0

x + 2 = 0 ⇒ x = - 2

x + 5 = 0 ⇒ x = - 5

roots are x = - 5 and x = - 2 with multiplicity 2