Question

Find an equation of a parabola that has the given numbers as solutions:

(2-3i), (2+3i)

I know it equals 13 but how do you find the equation?

Answer 1

your job it to multiply out
\[(x-(2-3i))(x-(2+3i))\] and that is not as hard as it looks. you already have the constant, it is
\[2^2+3^2=13\]

Answer 2

so all you need it the "middle term" which is
\[-2x-2x=-4x\] and that is it. your answer is
\[x^2-4x+13=0\] as the initial equation