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Math
Quadratic Equation
ax² + bx + c = 0, discriminant and roots
Runs locally in your browser
Parameters
Results
- D
- 1
- x₁
- 3
- x₂
- 2
How it works
Solves quadratic equations of the form ax² + bx + c = 0 using the discriminant and quadratic formula.
Who it's for: Algebra and pre-calculus students, engineers solving projectile motion, and anyone factoring second-degree polynomials.
Computes the discriminant D = b² − 4ac to determine the nature of the roots.
Returns two real roots when D > 0, one repeated root when D = 0, and reports complex roots when D < 0.
Displays x₁ and x₂ with up to four decimal places.
How to use
- Enter coefficients a, b, and c from your equation ax² + bx + c = 0.
- Ensure a ≠ 0 — if a is zero, the equation is linear, not quadratic.
- Read D (discriminant) to see whether roots are real or complex.
- Check x₁ and x₂ for the solution values when D ≥ 0.
Good to know
- Verify solutions by substituting back into the original equation.
- For systems of two linear equations, use the 2×2 Linear System calculator instead.
FAQ
- What if D is negative?
- The calculator reports Complex roots — there are no real solutions, but two complex conjugate solutions exist.