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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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