Algebra help for ACT!

J. The equation has one real solution and two complex solutions.

Step-by-step explanation:

Complex solutions come in pairs, so there can only be an even number of them.  So we can rule out G, H, and K.

To find the other roots, we can factor using either long division or grouping.  To use long division, see the attached picture.  To use grouping:

3x³ − 4x² + x − 10 = 0

3x³ − 6x² + 2x² + x − 10 = 0

3x² (x − 2) + (2x + 5) (x − 2) = 0

(x − 2) (3x² + 2x + 5) = 0

The other factor is 3x² + 2x + 5.  The discriminant of this is (2)² − 4(3)(5) = -56.  Since the discriminant is negative, the roots are complex.