The graph and degree of a polynomial with real coefficients fix) are given below

Question

The graph and degree of a polynomial with real coefficients fix) are given below. Determine the number of real zeros and the number of imaginary zeros. Assume Choose the correct answer below. that all the zeros of fix) are distinct. OA. There are two real zeros and three imaginary zeros O B. There is one real zero and four imaginary zeros. OC. There are two imaginary zeros 0 D. There are three real zeros. Degree 5 E. O F. There are three real zeros and two imaginary zeros. There are four real zeros and one imaginary zero y-fix)

Explanation / Answer

Real Zeros occur when the graph meets x-axis. There are 3 points where the graph meets x-axis. Hence, there are 3 real zeros. [ Since, it is given all roots are distinct, there are no repeated roots]

However, the degree of the polynomial is 5. So, there should be 5 roots.

Hence, the rest of the roots are complex roots. Therefore, there are 2 imaginary zeros.

Option (E) is correct.

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