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二次方程式ソルバーツール

Enter coefficients a, b, and c to solve the quadratic equation ax^2 + bx + c = 0 using the quadratic formula, with discriminant analysis, step-by-step work, and the vertex.

Last updated: 2026/10/16 Calculator Feedback & bug reports
Enter Coefficients

Enter the coefficients of ax^2 + bx + c = 0 (a must not be 0). Decimals and negatives are allowed.

Result
Enter coefficients and press "Calculate".

How to Use

1

Enter Coefficients

Enter coefficients a, b, and c for ax^2 + bx + c = 0 (a must be non-zero).

2

Calculate

Press the "Calculate" button to get the discriminant, roots, and their type.

3

Review the Steps

Check the quadratic-formula steps and the vertex, then copy as needed.

About Solving Quadratic Equations

A quadratic equation ax^2 + bx + c = 0 (a ≠ 0) is solved with the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a). The discriminant D = b^2 - 4ac determines the nature of the roots: D > 0 gives two distinct real roots, D = 0 gives one repeated root, and D < 0 gives two complex conjugate roots. This tool computes the discriminant, roots, and vertex automatically and shows the steps. Everything runs in your browser.

Features

  • Quadratic FormulaJust enter a, b, and c to solve instantly with the quadratic formula.
  • Root Type DetectionDetermines real, double, or complex roots from the discriminant sign.
  • Steps & VertexShows the substitution steps plus the parabola vertex and axis.
  • Privacy FirstAll processing happens in your browser. Nothing is sent to a server.

Use Cases

  • Checking quadratic-equation homework and exam prep
  • Understanding the quadratic formula and discriminant
  • Finding the vertex and axis of a parabola
  • Physics projectile motion and optimization problems
  • Verifying equations with complex (imaginary) roots

FAQ

What happens if I enter 0 for coefficient a?
When a = 0 the x^2 term disappears, so it becomes a linear equation rather than a quadratic one. The tool shows an error in that case. Please enter a non-zero value for a.
Can I use decimal or negative coefficients?
Yes. a, b, and c can be decimals or negative numbers. For example, a = 1.5, b = -3, c = 0.5 works fine.
What is the discriminant?
The discriminant D = b^2 - 4ac determines the type of roots. D > 0 means two distinct real roots, D = 0 means one repeated real root, and D < 0 means two complex conjugate roots.
Does it find complex (imaginary) roots?
Yes. When the discriminant is negative (D < 0), the tool shows the two complex conjugate roots in the form x = (-b ± √(4ac - b^2) i) / (2a).
Are my coefficients sent to a server?
No. All calculations run entirely in your browser, and the coefficients you enter are never sent to or stored on any external server.

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Related Guides

How to Solve Quadratic Equations: Formula, Discriminant, Factoring & Completing the Square Learn how to solve quadratic equations from the basics: the general form ax^2+bx+c=0, the quadratic formula, using the discriminant D=b^2-4ac to count real roots, solving by factoring, completing the square, and the link to the parabola graph.