SOLUTION: if the equation x^4+ax^2+bx+c=0 has roots 1,2,and 3 Find c

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: if the equation x^4+ax^2+bx+c=0 has roots 1,2,and 3 Find c      Log On


   

Question 382688: if the equation x^4+ax^2+bx+c=0 has roots 1,2,and 3 Find c
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial becomes
%28x-1%29%28x-2%29%28x-3%29%28x-r%29+=+0, where r is the fourth root. By Vieta's formulas, the sum of all roots of a polynomial ax%5En+%2B+bx%5E%28n-1%29+%2B+...+=+0 is -b/a. Since the x%5E3 coefficient is zero, the sum of all four roots is zero, so it follows that r = -6.
The polynomial is now %28x-1%29%28x-2%29%28x-3%29%28x%2B6%29+=+0. The constant term c is just (-1)(-2)(-3)(6) = -36.