Quadratic Formula
Also known as: Roots of Quadratic Equation
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
x = (-b ± √(b² - 4ac)) / 2aWhat It Calculates
Finds the solutions (roots) of any quadratic equation ax² + bx + c = 0. The discriminant b² - 4ac determines the number of real solutions.
variables
| Symbol | Name | Description |
|---|---|---|
| a | Coefficient of x² | Leading coefficient (must not be 0) |
| b | Coefficient of x | Linear coefficient |
| c | Constant | Constant term |
Derivation
Derived by completing the square on ax² + bx + c = 0: divide by a, move c/a to the right, add (b/2a)² to both sides, factor the left as a perfect square, then take the square root.
Worked Examples
1
Discriminant = 25 - 24 = 12
x = (5 ± 1) / 23
x = 3 or x = 2Result: x = 3, x = 2
Common Mistakes
Check that a ≠ 0 (otherwise it's linear, not quadratic)
If discriminant < 0, the roots are complex numbers
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