Question

If a polynomial equation p(x)=0 has 3+4i as a solution

3-i
4-3i
4+3i
3-4i

Answer 1

if 3 + 4 i is a solution
then its complex conjugate

3 - 4 i

is also a solution

because when you solve a quadratic for example
(- b +/- sqrt(b^2-4ac))/2a

if b^2-4ac is negative

then you have
-b + number*i
and
-b - same number*i
They come in complex conjugate PAIRS

Answer 2

Are you looking for another solution?
if so what do you think/

Answer 3

As Damon said, complex roots come in conjugate pairs.

Using properties of roots:
sum of our roots = 3+4i + 3-4i = 6
product of roots = (3+4i)(3-4i)
= 9 - 16i^2 = 25

p(x) = x^2 - 6x + 25