Difference between revisions of "Quadratic formula"
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− | The '''quadratic formula''' is a general [[expression]] for the [[ | + | The '''quadratic formula''' is a general [[expression]] for the [[root (polynomial)|solutions]] to a [[quadratic equation]]. It is used when other methods, such as [[completing the square]], [[factoring]], and [[square root property]] do not work or are too tedious. |
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===General Solution For A Quadratic by Completing the Square=== | ===General Solution For A Quadratic by Completing the Square=== | ||
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Let the quadratic be in the form <math>a\cdot x^2+b\cdot x+c=0</math>. | Let the quadratic be in the form <math>a\cdot x^2+b\cdot x+c=0</math>. | ||
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=== Variation === | === Variation === | ||
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In some situations, it is preferable to use this variation of the quadratic formula: | In some situations, it is preferable to use this variation of the quadratic formula: | ||
<math>\frac{2c}{-b\pm\sqrt{b^2-4ac}}</math> | <math>\frac{2c}{-b\pm\sqrt{b^2-4ac}}</math> |
Revision as of 21:58, 20 April 2008
The quadratic formula is a general expression for the solutions to a quadratic equation. It is used when other methods, such as completing the square, factoring, and square root property do not work or are too tedious.
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: