Question

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

x^3 − 2x^2 − 3x + 6
x^3 + 2x^2 − 3x − 6
x^3 − 3x^2 − 5x + 15
x^3 + 3x^2 − 5x − 15

Answer 1

If the roots are -sqrt(5), sqrt(5), and -3, then the three factors of the polynomial are: (x + sqrt(5)), (x - sqrt(5)), and (x+3) Let's multiply the first two factors together. (x + sqrt(5)) * (x - sqrt(5)) = x^2 - 5 Let's multiply this by the third factor (x+3). (x^2 - 5) * (x+3) = x^3 + 3x^2 -5x - 15 The correct answer is the last polynomial in the list of choices above.