Question

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

Answer 1

D

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