Question

select all correct answers.

1. one solution to a quadratic equation is ( x = -\frac{5}{3} ). which sentences could describe any remaining solutions?

there are no other real solutions because of repeated roots.
there is exactly one complex solution.
there are at least two more real solutions.
there is exactly one more real solution.
there are two or more complex solutions.
there are no complex solutions.

Explanation:

A quadratic equation has exactly 2 roots (counting multiplicities) over the complex numbers. If one real solution is a repeated root (a double root), there are no other distinct real solutions, and complex roots for quadratics come in conjugate pairs, so there can't be a single complex solution. A repeated real root means the quadratic has only that one distinct real solution, no other real or complex solutions.

Answer:

A. There are no other real solutions because of repeated roots.
F. There are no complex solutions.