Quadratic Equation Solver
Enter coefficients a, b, and c of ax² + bx + c = 0 to instantly get roots, discriminant, and solution type.
How It Works
Applies the quadratic formula. Discriminant (b²−4ac) determines whether roots are real, repeated, or complex.
Formula
x = (−b ± √(b²−4ac)) / 2a
Δ = b²−4ac: >0 = two real roots | =0 = one root | <0 = complex roots
Example
x²−5x+6=0 (a=1, b=−5, c=6):
Δ = 1 > 0 → x&sub1;=3, x&sub2;=2
When to Use This Calculator
Use for algebra homework, physics projectile problems, or any equation reducible to quadratic form.
Common Mistakes to Avoid
- Not moving all terms to one side first — must equal 0.
- Using a=0 — that makes it linear, not quadratic.
- Sign errors on b — in 2x²−3x+1, b=−3.
Frequently Asked Questions
What does the discriminant tell me?
b²−4ac > 0: two real roots. = 0: one repeated root. < 0: complex roots.
What are complex roots?
Involve imaginary numbers (i=√−1). Appear as a ± bi pairs.
Works for degree 3?
No — cubic equations need different methods.
How to verify?
Substitute root back into original equation and confirm it equals 0.
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Last Updated: July 4, 2026