Difference between revisions of "Quadratic formula"
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| − | The quadratic formula is used to simplify the process of solving a quadratic equation. | + | The '''quadratic formula''' is used to simplify the process of solving a [[quadratic equation]]. |
| − | : | + | First, the quadratic equation must be reduced to this format: |
| − | |||
| − | |||
:<math>ax^2+bx+c=0\!</math> | :<math>ax^2+bx+c=0\!</math> | ||
| − | + | Then the coefficients ''a'', ''b'', and ''c'' can be substituted in the formula to find the solutions: | |
| + | |||
| + | :<math>x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}</math> | ||
| + | |||
| + | You can prove that the formula is correct by substituting the formula in place of '''x''' in <math>ax^2+bx+c=0\!</math> and then gradually simplifying the rather complicated formula that results, step by step. Eventually, if all the steps are done correctly, it will simplify to 0. | ||
| − | + | Derivation of the formula is usually done via the method of [[completing the square]]. | |
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Revision as of 17:58, April 22, 2007
The quadratic formula is used to simplify the process of solving a quadratic equation.
First, the quadratic equation must be reduced to this format:
- <math>ax^2+bx+c=0\!</math>
Then the coefficients a, b, and c can be substituted in the formula to find the solutions:
- <math>x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}</math>
You can prove that the formula is correct by substituting the formula in place of x in <math>ax^2+bx+c=0\!</math> and then gradually simplifying the rather complicated formula that results, step by step. Eventually, if all the steps are done correctly, it will simplify to 0.
Derivation of the formula is usually done via the method of completing the square.