Question

find the polynomial of degree 5 with integer coefficients, and zeros 1/2 , -2 and i, and leading coefficient 2; the zero -2 has multiplicity 2.

Answer 1

good lord. ok taking care of zeros one at a time we get
\[(2x-1)(x+2)^2(x-i)(x+i)\] now you get to multiply. not too bad especially since
\[(x+i)(x-i)=x^2+1\]