Can a polynomial have four solutions but only two x-intercepts? In 1-2 sentences, explain how this can or cannot occur.

Answer 1

Yes, a polynomial can have four solutions but only two x-intercepts if the solutions include complex roots or repeated real roots. For example, a polynomial of degree four could have two distinct real roots (x-intercepts) and two complex conjugate roots, or it could have a repeated real root (with multiplicity two) resulting in only two x-intercepts.