The complex numbers 1+i and 1+2i are both roots of the equation
x^5-6x^4+Ax^3+Bx^2+Cx+D=0
Where A B C D are integers. What is the value of A+B+C+D

Question

The complex numbers 1+i and 1+2i are both roots of the equation 
x^5-6x^4+Ax^3+Bx^2+Cx+D=0
Where A B C D are integers. What is the value of A+B+C+D

precal · Answer

if you know that 1+i is a solution, you can assume 1-i is a solution

precal · Answer

1+2i and 1-2i are solutions 
complex conjugate theorem allows us to assume those soltuions

precal · Answer

means 4 solutions are complex, you are just missing 1 solution due to the 5th power and it is real

anonymous · Answer

I got there. I have that x^4-4x^3+11x^2-14x+10 is a factor of that unknown equation.

precal · Answer

I am not sure what to do to help you find that last solution

anonymous · Answer

I sholud've known that if precal was here, a medal would already be taken :)

anonymous · Answer

ok...

precal · Answer

|dw:1356904110379:dw|I know you have to multiply all of those out