Question 431282
The quadratic will have {{{x - (4+2i) = x - 4 - 2i}}} and {{{x - (4-2i) = x - 4 + 2i}}} as factors. Hence, the quadratic is equal to {{{(x - 4 - 2i)(x - 4 + 2i) = ((x - 4) - 2i)((x - 4) + 2i) = (x - 4)^2 - (2i)^2}}} (applying the difference of two squares)


Expanding and simplifying, this is equal to {{{x^2 - 8x + 16 + 4 = x^2 - 8x + 20}}}.