Question

Which of the following is a polynomial with roots: − square root of 5 , square root of 5 , and −3?

A: x^3 − 2x^2 − 3x + 6

B: x^3 + 3x^2 − 5x − 15

C: x^3 − 3x^2 − 5x + 15

D: x^3 + 2x^2 − 3x − 6

Answer 1

roots: - √5 , √5, and - 3

=> these are factors of the polynomial: (x + √5), (x - √5), and (x + 3).

Multiply those three factors:

(x + √5) (x - √5) ( x + 3) = [x^2 - 5] ( x + 3 ) = x^2 + 3x^2 - 5x - 15

Therefore the polynomial x^2 + 3x^2 - 5x - 15 is a polynomial with the given roots.

Answer: option B. x^3 + 3x^2 - 5x - 15