Form a Polynomial f(x) with real coefficients

Question

hi! please solve this for me(:

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

Degree 4; zeros 5+4i , 3 multiplicity 2

Answer: f(x)= a ( ) ???

Answer 1

P(x) = (x-3)^2 ( (x-5)+4i) ((x-5)-4i)

= (x-3)^2 [ (x-5)^2 + 16]

= (x-3)^2 [ x^2 - 10x + 41]

= (x^2 - 6x + 9)(x^2-10x+41)