PRECAL MATH HW chapter 6

Question

Find a polynomial with rational coefficients of minimal degree passing through (−2,7) and having zeros

1, 1/2, 1/2, 1 , − squareroot of 2i, 2 + squareroot 3𝑖.

Answer 1

f = a(x-1)^2(x-1/2)^2(x^2+2)(x^2-4+7)

a = 28/12825 = about .002