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Last updated: July 31, 2026

Discriminant Calculator

Dharmendra Singh - Creator

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Balram Rajput
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Formula

Δ = b² - 4ac

Where:

  • a,b,c=Quadratic coefficients in ax²+bx+c=0
Discriminant and Root TypesThree parabolas illustrate how the sign of the discriminant determines the number of real roots.D > 0Two real rootsD = 0One repeated rootD < 0Complex rootsD = b² - 4ac
The discriminant's sign tells you whether a quadratic has two real, one repeated, or two complex roots.

Worked Examples

Two distinct real roots

For x²-3x+2=0.

  1. 1Δ = (-3)² - 4(1)(2)
  2. 2Δ = 9 - 8 = 1
  3. 3Δ>0 so two distinct real roots
Final Answer: discriminant=1, rootType="Two distinct real roots"

Repeated root

For x²+2x+1=0.

  1. 1Δ = 2² - 4(1)(1)
  2. 2Δ = 4 - 4 = 0
  3. 3Δ=0 so one repeated real root
Final Answer: discriminant=0

Complex conjugate roots

For x²+1=0.

  1. 1Δ = 0² - 4(1)(1)
  2. 2Δ = -4
  3. 3Δ<0 so roots are complex conjugates
Final Answer: discriminant=-4, rootType="Two complex conjugate roots"

Introduction

This calculator computes the quadratic discriminant and instantly classifies the equation’s root type.

Formula and Method

The Discriminant Calculator uses the core relation Δ = b² - 4ac.

  • Apply the formula directly to user inputs

  • Compute intermediate terms when needed

  • Round numeric outputs for stable display

  • Return structured outputs for UI rendering

Input Fields

Provide values for: a, b, c.

  1. 1

    a: a

  2. 2

    b: b

  3. 3

    c: c

Output Fields

The calculator returns: discriminant, rootType.

  1. 1

    discriminant: Value of b²-4ac

  2. 2

    rootType: Classifies roots from sign of Δ

Validation Rules

a, b, and c must be numeric, and a cannot be 0.

  • Invalid or missing numeric values trigger safe fallback outputs

  • Error messaging is returned by the calculation function when constraints fail

  • Domain restrictions are enforced before formula evaluation

  • Rounding is applied to final numeric values

How to Use This Calculator

Enter valid inputs, run the calculation, and review both primary and supporting outputs.

  • Enter each required field

  • Click calculate

  • Check primary output first

  • Use examples to verify expected behavior

Practical Uses

This calculation is commonly used in math practice, engineering checks, and fast verification tasks.

  • Homework and exam preparation

  • Quick sanity checks while modeling

  • Teaching and tutoring demonstrations

  • Reusable reference for manual calculations

FAQs

What does the Discriminant Calculator compute?

It computes discriminant, rootType from the provided inputs.

Which inputs are required?

Required fields are a, b, c.

How are results rounded?

Numeric outputs are rounded by the calculation function (generally to about 6 decimal places) for cleaner display.

What if I enter invalid values?

a, b, and c must be numeric, and a cannot be 0.

Which output should I read first?

Start with discriminant, then use the remaining outputs for context and interpretation.

Can I use decimal values?

Yes. Decimal inputs are supported unless the calculator specifically requires integer-style values.

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