What is the equation of f(x) if (3-5i) and (3+5i) are the roots?

Let the equation be f(x) = x^2 + bx +
c

Then we know that if x1 and x2 are the roots of
f(x).

Then x1+x2=
-b/a

==> x1*x2= c/a

We
have the roots (3-5i) and (3+5i)

==> (3-5i)+(3+5i) =
6 = -b ==> b= -6

==> (3-5i)(3+5i)= 9+25= 34 =
c

==> f(x)= x^2 - 6x + 34 =
0

To check we will calculate the
roots.

==> x1= (6+sqrt(-100) / 2 = 6+10i / 2 = 3+
5i

==> x2=
3-5i

Then the equation is: f(x) = x^2 -6x +
34