Find a quadratic function with real coefficients whose zeros include 1+the square root of 3i.

Answer 1

since the coefficients are all real, the complex roots must come in conjugate pair. So the minimum polynomial would be

y = (x-(1+√3 i))(x-(1-√3 i))
= ((x-1)-√3 i)((x-1)+√3 i)
= (x-1)^2 - (√3 i)^2
= x^2-2x+1 + 3
= x^2-2x+4