SOLUTION: The equation x^2 + Bx + C = 0 has 5 as the sum of its roots and 15 as the sum of the squares of the roots. What is the value of C?

Let the roots be r and s.

Then B = -(r+s) and C = rs

Since the sum of the roots is 5,

B = -(r+s) = -(5) = -5

So

r+s = 5

Squaring both sides:







The sum of the squarse of the roots is 15 so
we replace  by 15







and since C = rs

C = 5

Edwin