For a polynomial f (x) with real coefficients having the given degree and zeros.

Question

Degree 4; zeros 4+2i ; 4 multiplicity 2

Answer 1

the complex roots occur in conjugate pairs, so 4-2i is also a root. So,
f(x) = (x-4)^2 (x-(4+2i)) (x-(4-2i))
= (x-4)^2 ((x-4)-2i)((x-4)+2i)
= (x-4)^2 ((x-4)^2 - (2i)^2)
= (x-4)^2 (x^2-8x+16 + 4)
= (x-4)^2 (x^2-8x+20)