June 17th
June 17th
Sum of the Roots of a Quadratic
To find the sum of the roots of a quadratic ax 2 +
bx + c = 0, use the formula:
Example
Find the sum of the roots of 3x 2 + 9 x = 13. First
of all, make sure that both the ax 2 and bx terms appear on the
same side. If they do not appear on the same side, then the sum
of the roots is just b/a (without the negative). Here, the sum of
the roots is 
Proof
Let the quadratic be ax 2 + bx + c = 0 with roots r
and s . Then from the quadratic formula, we have
Then, the sum of the roots is
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