Quadratic Formula Calculator
Solve real roots of ax² + bx + c = 0 from three coefficients and inspect the discriminant used to classify the result.
Solve a quadratic equation
How this tool works
A quadratic equation has a non-zero squared-term coefficient and may have two, one, or no real roots. This calculator evaluates the discriminant first and then applies the quadratic formula when real solutions exist.
The discriminant is b²−4ac. Real roots are (−b ± √discriminant)/(2a); a positive discriminant gives two roots, zero gives one repeated root, and negative gives none in the real numbers.
How to use it
- Enter coefficients a, b, and c from ax² + bx + c = 0.
- Ensure coefficient a is not zero.
- Review the real roots and discriminant classification.
Worked examples
Two distinct roots
- Input
- a=1, b=-3, c=2
- Output
- Roots 2 and 1
The discriminant is one. Substituting plus and minus its square root into the quadratic formula produces the two real roots two and one.
No real roots
- Input
- a=1, b=0, c=1
- Output
- No real roots
The discriminant is negative four, so its square root is not real. The current calculator reports that classification rather than complex-number roots.
Limitations
- The current output does not express complex-number roots.
- Floating-point rounding may slightly approximate irrational solutions.