Question 261699
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?
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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:

{{{(r+s)^2=5^2}}}

{{{r^2+2rs+s^2=25}}}

{{{(r^2+s^2)+2rs=25}}}

The sum of the squarse of the roots is 15 so
we replace {{{r^2+s^2}}} by 15

{{{15+2rs=25}}}

{{{2rs=10}}}

{{{rs=5}}}

and since C = rs

C = 5

Edwin</pre>