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?

I know The correct answer is 6. I need help with the explanation please.

Answer 1

Note that the two maxima lie on the x-axis. So, they are double roots. Both are real.

Now add to that the complex root and its conjugate, and you have degree 6.