Question

what type of roots does the polynomial have? three imaginary; one real, and two imaginary; three real; two real and one imaginary

Explanation:

Step1: Analyze polynomial graph

A polynomial's real roots correspond to its x-axis intercepts.

Step2: Count x-intercepts

The provided graph crosses the x-axis 3 distinct times, meaning there are 3 real roots.

Step3: Match to options

This matches the "Three real" choice, as a cubic polynomial can have 3 real roots (no imaginary roots needed here, since imaginary roots come in pairs).

Answer:

Three real