Quadratic formula
The solutions of a x² + b x + c = 0. History: 7th to 9th century in its modern form.
How to work it out
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The statement:
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The solutions of a x² + b x + c = 0.
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Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]Worked examples (computed)
| Equation | Discriminant | Solutions |
|---|---|---|
| x² - 5x + 6 = 0 | 1 | 3, 2 |
| x² + 2x + 1 = 0 | 0 | -1 |
| 2x² - 3x - 2 = 0 | 25 | 2, -1/2 |
| x² + 1 = 0 | -4 | i, -i |
| x² + x - 1 = 0 | 5 | (-1 + √5)/2, (-1 - √5)/2 |
Questions
What is the quadratic formula?
The solutions of a x² + b x + c = 0.
Who is the Quadratic formula associated with?
Brahmagupta, Al-Khwarizmi.