Difference between revisions of "Quadratic formula"
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Given the values <math>{a},{b},{c}</math>, we can find all [[real]] and [[complex number|complex]] solutions to the quadratic equation. | Given the values <math>{a},{b},{c}</math>, we can find all [[real]] and [[complex number|complex]] solutions to the quadratic equation. | ||
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+ | === Variation === | ||
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+ | <math>\frac{2c}{-b\pm\sqrt{b^2-4ac}}</math> | ||
+ | |||
+ | In some situations, it is preferable to use this variation of the quadratic formula. |
Revision as of 23:08, 31 October 2006
The quadratic formula is a general expression for the solutions to a quadratic equation.
General Solution For A Quadratic by Completing the Square
Let the quadratic be in the form .
Moving c to the other side, we obtain
Dividing by and adding
to both sides yields
.
Factoring the LHS gives
As described above, an equation in this form can be solved, yielding
This formula is also called the quadratic formula.
Given the values , we can find all real and complex solutions to the quadratic equation.
Variation
In some situations, it is preferable to use this variation of the quadratic formula.