Which of the following is a polynomial with roots - square root of 5, square root of 5, and - 3? x3 - 2x2 - 3x + 6, x3 + 2x2 - 3x - 6, x3 - 3x2 - 5x + 15, or x3 + 3x2 - 5x - 15?

The fourth option.

The roots of x^3 + 3x^2 - 5x - 15 are - 3, + √5 and - √5.

To find the roots you can factor the polynomial in this way:

x^3 + 3x^2 - 5x - 15 = x^2 (x + 3) - 5 (x + 3) = (x + 3) (x^2 - 5)

The roots are the values of x that make the function = 0.

Then the roots are

x + 3 = 0 = = > x = 3, and

x^2 - 5 = 0 = = > x = + / - √5.