college algebra
posted by ladybug .
form a polynomial f (x) with real coefficients having the given degree and zeros.
degree 5; zeros 5; i; 6+i
f(x)= a(?)
Please show step by step work.

since complex roots come in pairs, the factors are
(x5)(xi)(x+i)(x(6+i))(x(6i))
(x5)(xi)(x+i)((x6)i)((x6)+i)
(x5)(x^2+1)(x^2+12x+37)