Thread: Zeros of a polynomial View Single Post
 P: 1,996 1. The problem statement, all variables and given/known data Find the zeros of the polynomial $$P(x) = x^4-6x^3+18x^2-30x+25$$ knowing that the sum of two of them is 4. 2. Relevant equations http://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formulas 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: $$x_1+x_2+x_3+x_4 = 6$$ $$x_1 x_2 +x_1 x_3 +x_1 x_4 + x_2 x_3 + x_2 x_4 +x_3 x_4 = 18$$ $$x_1 x_2 x_3 + x_1 x_3 x_4 +x_2 x_3 x_4 +x_1 x_2 x_4= 30$$ $$x_1 x_2 x_3 x_4 = 25$$ 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.