Find a degree 4 polynomial with real coefficients having zeros at x=2 with multiplicity 2, at x=1-2i with multiplicity 1, and with y-intercept at (0,-40)

Question

Keep in factored form.

Answer 1

-2(x-2)²(x²+5)

Multiplicity 2 means the root is in a squared term.

The complex root must have its conjugate as a root....that gives you the factor with a 5 in it.

The -2 gets you the -40.