Sum of the Roots of a Quadratic
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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finding LCM and GCF |
|
operations with complex numbers (simplifying, rationalizing complex denominators...) |
|
solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations) |
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solving a system of two and three linear equations (including Cramer's rule) |
|
graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions) |
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graphing general functions |
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operations with functions (composition, inverse, range, domain...) |
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simplifying logarithms |
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arithmetic and other pre-algebra topics (ratios, proportions, measurements...) |
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