Question 1138496
the third zero is 2-i, since complex roots are conjugate.

(x+2)(x-2-i)(x-2+i) are factors
multiply the second and third.
x^2-2x+ix. -2x+4-2i. -ix+2i-i^2
This is x^2-4x+5, remembering that i^2 is -1, so that -i^2=+1
the polynomial is x^3+2x^2-4x^2-8x+5x+10=x^3-2x^2-3x+10
a(x^3-2x^2-3x+10) has to give a y-intercept of -20
so a is -2
-2x^3+4x^2+6x-20 is the polynomial.

{{{graph(300,300,-10,10,-30,30,-2x^3+4x^2+6x-20)}}}