Quadratic Equation Solver

Q: "What is the quadratic formula?"

"x = (−b ± √(b² − 4ac)) / (2a) for ax² + bx + c = 0."

Q: "What if b² − 4ac is negative?"

"The roots are complex (non-real). The calculator shows them as real part ± imaginary part."

Q: "What if a is zero?"

"Then it is not quadratic (linear). Enter a non-zero a."

Q: "Can I get one root (repeated)?"

"Yes. When b² − 4ac = 0, there is one repeated real root (discriminant zero)."

Q: "What about rounding?"

"Results are rounded to a few decimal places. Exact rational roots may show as decimals."

Solve ax² + bx + c = 0. Example: a=1, b=-3, c=2 → x = 1 or 2. Real or complex roots. Copy result.

Quadratic equation ax² + bx + c = 0 has roots x = (−b ± √(b² − 4ac)) / (2a). Enter a, b, and c (a ≠ 0). The calculator gives real or complex roots. Copy the result or Copy with labels.

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Examples

a=1, b=-3, c=2 → x = 1, x = 2
a=1, b=0, c=-1 → x = 1, x = -1
a=1, b=2, c=5 → complex roots

FAQ

What is the quadratic formula?

x = (−b ± √(b² − 4ac)) / (2a) for ax² + bx + c = 0.

What if b² − 4ac is negative?

The roots are complex (non-real). The calculator shows them as real part ± imaginary part.

What if a is zero?

Then it is not quadratic (linear). Enter a non-zero a.

Can I get one root (repeated)?

Yes. When b² − 4ac = 0, there is one repeated real root (discriminant zero).

What about rounding?

Results are rounded to a few decimal places. Exact rational roots may show as decimals.