form a polynominal f(x) with real coefficients given the following degree 5; zeros: -7;-i;-3+i

Question

form a polynominal f(x) with real coefficients given

  Degrees 5; zeros:-7; -i;-3+i

f(x)=a(     )

Answer 1

The missing complex zeroes are i and -3-i, because they will "cancel out" the given complex zeroes.

The polynomial f(x)=(x+7)(x^2+1)(x^2+6x+10)=a(x^5+13x^4+53x^3+83x^2+52x+70), where a is a real number.