Find a polynomial (with real coefficients) of degree 4 with zeros at - 3 (multiplicity of 2) and - 2i, and with 6 as the coefficient of x

Step-by-step explanation:

If - 2i is a root, then so is + 2i, so

y = a (x+3) ^2 (x^2+4)

= a (x^4+6x^3+13x^2+24x+36)

Since we want 24a = 6, our final polynomial is

y = 1/4 (x^4+6x^3+13x^2+24x+36)