Why use this calculator
Quadratic equations appear throughout mathematics, physics, engineering, and economics. This solver handles all cases including complex roots.
How to use it
Enter the coefficients a, b, and c for the equation ax² + bx + c = 0. The calculator finds the roots and identifies their nature.
The formula
x = (-b ± √(b²-4ac)) / 2a. The discriminant (b²-4ac) determines the nature of roots: positive = 2 real, zero = 1 repeated, negative = 2 complex.
Worked examples
x² - 5x + 6 = 0
x = 3 and x = 2
x² + 1 = 0
x = i and x = -i (complex roots)
When people use it
- Algebra coursework
- Physics trajectory problems
- Engineering calculations
- Optimization problems
Tips
- Check your answer by substituting roots back into the equation
- The vertex of the parabola is at x = -b/(2a)
- Complex roots always come in conjugate pairs
Questions people ask
- What does the discriminant tell us?
- If b²-4ac > 0: two distinct real roots. If = 0: one repeated root. If < 0: two complex conjugate roots (no real solutions cross the x-axis).