SOLUTION: 1)Use the Cauchy - Schwarz inequality to solve x3 ─ 25x2 ─ 4x + 100 = 0, given that all its roots are rational. (5 Marks

Algebra ->  Inequalities -> SOLUTION: 1)Use the Cauchy - Schwarz inequality to solve x3 ─ 25x2 ─ 4x + 100 = 0, given that all its roots are rational. (5 Marks       Log On


   



Question 408068: 1)Use the Cauchy - Schwarz inequality to solve x3 ─ 25x2 ─ 4x + 100 = 0, given that all its roots are rational. (5 Marks
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I don't really see how the Cauchy-Schwarz inequality applies to this problem...from what I know, the Cauchy-Schwarz inequality says that for positive numbers a%5Bi%5D and b%5Bi%5D, 1+%3C=+i+%3C=+n,

.

The best way is to factor x+-+25 out, leaving

%28x+-+25%29%28x%5E2+-+4%29+=+0

From here, it is apparent that x = 25, -2, or 2.