Discriminant Calculator
The core tool. Compute D = b² – 4ac and instantly see the nature of roots with step-by-step working.
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A complete suite of quadratic equation calculators — all free, instant, and step-by-step.
Nature of Roots Calculator
Input a, b, c and get a clear classification: two real, one repeated, or two complex roots.
Use ToolQuadratic Formula Calculator
Solve ax² + bx + c = 0 fully. Get both root values x₁ and x₂ using x = (−b ± √D) / 2a.
Use ToolPolynomial Discriminant
Extend the discriminant concept to cubic and higher-degree polynomials.
Use ToolParabola / Graph Calculator
Visualize the parabola of your quadratic. See vertex, axis of symmetry, and x-intercepts.
Use ToolDiscriminant with Steps
Extra-annotated, exam-ready discriminant calculator with every intermediate step shown.
Use ToolCompleting the Square
Rewrite any quadratic in vertex form by completing the square — shown step by step.
Use ToolVertex Form Calculator
Convert standard quadratic form to vertex form a(x–h)² + k to find the vertex directly.
Use ToolSum & Product of Roots
Use Vieta's formulas to calculate the sum (–b/a) and product (c/a) of roots without solving.
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Completely Free
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Instant Results
Results appear immediately — no page reloads, no waiting. Pure client-side speed.
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Step-by-Step
Every calculation includes a full working so you understand, not just copy-paste.
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Mobile Friendly
Works perfectly on any device — phone, tablet, or desktop. Fully responsive layout.
Need Help Understanding the Discriminant?
Read our beginner-friendly guides on the blog, or jump straight to the calculator.
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