Which correctly describes the roots of the following cubic equation x^3-5x^2+3x+9=0? a. three real roots, each with a different value b. one real root and to complex roots c. three real roots, two of which are equal in value d. 2 real roots and one complex root?

The correct answer is letter C, because you have to calculate de discriminating which is 18abcd-4b^3d+b^2c^2-4ac^3-27a^2d^2 = 0
For your equation a=1, b=-5, c=3, d=9
So when the discriminating is equal zero, the equation has 3 real roots, two of which are equal in value.
You can prove this solving your equation using Ruffini's Rule and you will get the roots are: 3, 3, and -1