1. The problem statement, all variables and given/known data
Find the zeros of the polynomial
[tex]P(x) = x^4-6x^3+18x^2-30x+25[/tex]
knowing that the sum of two of them is 4.
2. Relevant equations
3. The attempt at a solution
Let x_1,x_2,x_3,x_4 be the complex roots and let x_1 +x_2 = 4. Here are the Viete relations in this case:
[tex]x_1+x_2+x_3+x_4 = 6 [/tex]
[tex] x_1 x_2 +x_1 x_3 +x_1 x_4 + x_2 x_3 + x_2 x_4 +x_3 x_4 = 18 [/tex]
[tex] x_1 x_2 x_3 + x_1 x_3 x_4 +x_2 x_3 x_4 +x_1 x_2 x_4= 30 [/tex]
[tex] x_1 x_2 x_3 x_4 = 25[/tex]
The first one implies that x_3 +x_4 =2. And then the second one implies that x_1 x_2 + x_3 x_4 = 10 but that is as far as I can get.
Please just give a hint.