Question

Does anyone know how to find this?
Find the polynomial function with roots 11 and 2i.

Answer 1

Okay, if the polynomial has only real coefficients (I assume so) then any complex roots must come in conjugate pairs \((a + bi, a - bi)\). We know each root contributes a product term \((x-r) = 0\) so our polynomial can be written as

\[f(x) = (x-11)(x-2i)(x+2i)\]
Multiply that out and collect terms. I suggest multiplying the two complex binomials first.