Quadratic Formula Calculator
Using the Quadratic Formula
The quadratic formula is used to find the roots of a quadratic equation in the form \(ax^2+bx+c=0\).
The Formula:
\[ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \]
The Discriminant:
The part of the formula under the square root, \(\Delta = b^2-4ac\), is called the discriminant. It tells us about the nature of the roots:
- If \(\Delta > 0\), there are two distinct real roots.
- If \(\Delta = 0\), there is exactly one real root (a repeated root).
- If \(\Delta < 0\), there are two complex conjugate roots.
Solves \(ax^2+bx+c=0\) and shows the steps.
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