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Quadratic Equation Solver

Math Calculators

Discriminant, real/complex roots and vertex

Quick Answer

Quadratic Equation Solver: Discriminant, real/complex roots and vertex. Quadratic Equation Solver uses standard math formulas to compute accurate results instantly.

ax² + bx + c = 0

Presets:

Two real roots

x₁ = 3，x₂ = 2

Δ = b²−4ac1
x₁ + x₂ (Vieta)5
x₁ · x₂ (Vieta)6
Vertex(2.5, -0.25)

Quadratic formula steps

  1. 1Δ = b² − 4ac = (-5)² − 4×1×6 = 1
  2. 2Δ > 0 → two distinct real roots
  3. 3x = (−b ± √Δ) / 2a = (5 ± 1) / 2
  4. 4Vertex at x = −b/2a = 2.5, y = -0.25
  5. 5Parabola opens upward (minimum)

Graph features

Axis of symmetryx = 2.5
DirectionUpward (a > 0)
ExtremumMin = -0.25
y-intercepty = 6
x-intercepts2 points

💡 Vieta's formulas: x₁+x₂ = −b/a, x₁·x₂ = c/a — use them to verify roots instantly without solving. For systems of equations use the Equation Solver.

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How to Use

  1. Enter values or expressions: type directly into the Quadratic Equation Solver — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Quadratic Equation Solver is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Discriminant, real/complex roots and vertex.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Quadratic Equation Solver formula

Quadratic Equation Solver uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Quadratic Equation Solver?
Open the page and fill in the input fields — results update automatically. Discriminant, real/complex roots and vertex.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

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Cite this page: YiJianSuan. Quadratic Equation Solver[EB/OL]. https://www.yijiansuan.com/en/c/math/quadratic

Results provided by this tool are for reference only and do not constitute professional advice.