the Degree 5; zeros: -6; -i; -3+i

Question

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

Answer 1

The polynomial can be derived from (x+6)(x+i)(x-i)(x+3-i)(x+3+i)=

(x+6)(x^2+1)(x^2+6x+10)=

(x^3+x+6x^2+6)(x^2+6x+10)=

x^5+6x^4+10x^3+x^3+6x^2+10x+6x^4+36x^3+60x^2+6x^2+36x+60=

x^5+12x^4+47x^3+72x^2+46x+60. This a degree 5 polynomial with zeroes: 6, i, -i, -3+i, -3-i.