The Quadratic Formula
The quadratic formula is one of the most important formulas in all of mathematics:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
It solves ANY quadratic equation \( ax^2 + bx + c = 0 \).
Breaking It Down
- \( -b \): The negative of the coefficient of x
- \( \pm \): Gives two solutions (plus and minus)
- \( b^2 - 4ac \): The discriminant ΓÇö tells you the nature of roots
- \( 2a \): The denominator
The Discriminant
- \( \Delta > 0 \): Two real solutions
- \( \Delta = 0 \): One repeated solution
- \( \Delta < 0 \): Two complex solutions
See the formula in action on our solver!
