Question

The graph of a rational function has a local maxima at (-1,0) and (8,0). The complex number 2+3i Is a zero of the function. What is the least possible degree of the function

Answer is 6

But i need help with an explanation.

Answer 1

Since the maxima are on the x-axis, they must be roots of even multiplicity. There must be a conjugate root as well, so that makes at least 6 roots.