Question

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

Explanation:

Step1: Analyze graph x-axis intersections

A polynomial's real roots correspond to where its graph crosses the x-axis.

Step2: Count visible x-axis crossings

The provided graph crosses the x-axis 3 distinct times.

Step3: Match to root type

A cubic polynomial (degree 3) has 3 roots (counting multiplicities). Since we see 3 real crossings, all roots are real.

Answer:

D. Three real