Degree is 4, zeros at x= -1,1/2, and 1-i, leading coefficient is 2

Question

Just need to find the polynomial

Answer 1

roots -1, 1/2 1-i, 1+i, imaginary roots come in conjugate pairs

2(x+1)(x-1/2)(x-1+i)(x-1-i)

expand

(x+1)(2x-1)(x^2 -(1-i)(1+I))

= (2x^2 +x-1)(x^2 -2x+2)

= 2x^4 -4x^3 +4x^2 +x^3 -2x^2 +2x -x^2 +2x-2

= 2x^4-3x^3 +x^2 +4x -2