Find a polynomial f(x) of degree 4 with real coefficients and the following zeros.

Question

-1 (multiplicity 2), -3+2i

Answer 1

f=(x+1)^2(x^2-6x+13)

(x^2+2x+1)(x^2-6x+13)

= x^4 -4x^3 +2x^2 +20x +13 is the 4th degree polynomial with the given zeros

x=-3+2i

x+3=2i

x^2+6x+9=-4

x^2+6x+13 is one factor

x=-1

x+1 is another

x+1 is a 3rd factor

mulyiply the 3 together