Consider the roots of a cubic equation with integral coefficients: - 1, - 4, and 3. Which choice is a factor of the cubic equation? A) x + 3 B) x - 1 C) x - 4 D) x - 3

Question

April Carroll

Mathematics

9 July, 13:29

Consider the roots of a cubic equation with integral coefficients: - 1, - 4, and 3. Which choice is a factor of the cubic equation? A) x + 3 B) x - 1 C) x - 4 D) x - 3

+3

Answers (1)

Know the Answer?

Cordell Moran · Answer 1

D

Step-by-step explanation:

Lets go case by case.

Given the roots, a factor will be part of the equation if for some of the roots the factor becomes null, i. e., equal to 0.

Is there any root that makes (x+3) = 0? No, as it only becomes 0 for x = - 3 and - 3 is not a root. So A NO!

Is there a root that makes (x-1) = 0? No, as it only becomes 0 for x=1 and 1 is not a root. So B NO!

(x-4) = 0 only for x=4, and as 4 is not a root, C NO!

The last, (x-3) = 0 if x=3. As 3 is one of the roots, (x-3) is a factor of our equation!

D is the only correct option!