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Algebra

Discriminant Calculator

b² − 4ac for ax²+bx+c. Free online Discriminant Calculator. Calculate discriminant online — fast, accurate, mobile-friendly, no signup needed.

Discriminant
1

Derivation

  1. ├── 01Givena = 1, b = -5, c = 6
  2. ├── 02Formulaa²-4 × t × e.c
  3. ├── 03Substitute1²-4 × t × e.6
  4. └── 04Compute Discriminant1
Did you know?

The quadratic formula goes back to Babylonian scribes c. 2000 BCE; al-Khwārizmī gave it in words in 820 CE; Viète wrote it in algebraic symbols in 1591.

§01What is

Understanding the Discriminant Calculator

The Discriminant Calculator computes Discriminant from 3 inputs: a, b, c. b² − 4ac for ax²+bx+c.

Algebra is the art of solving for the unknown. Rearranging a formula to isolate the variable you actually need is the single most common real-world math skill — and doing it with real numbers under time pressure is where errors happen. The Discriminant Calculator sits in that toolkit — it b² − 4ac for ax²+bx+c. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

a²-4 × t × e.c

Where

a
a
b
b
c
c
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: a = 1, b = -5, c = 6.

  1. 01Start by noting the input — a: 1.
  2. 02Start by noting the input — b: -5.
  3. 03Start by noting the input — c: 6.
  4. 04Substitute these values into the formula: a²-4 × t × e.c
  5. 05Compute Discriminant: the calculator returns 1.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Discriminant Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

a halved

a = 0.5 (from 1)

Keep every other input at its default and halve the a. See how discriminant responds.

  1. 01New a: 0.5
  2. 02Baseline Discriminant: 1
  3. 03New Discriminant: 13
  4. 04Discriminant increases by 1200% → use this sensitivity to plan for real-world variation.
02 · PATTERN

a doubled

a = 2 (from 1)

Keep every other input at its default and double the a. See how discriminant responds.

  1. 01New a: 2
  2. 02Baseline Discriminant: 1
  3. 03New Discriminant: -23
  4. 04Discriminant decreases by 2400% → use this sensitivity to plan for real-world variation.
03 · PATTERN

b halved

b = -2.5 (from -5)

Keep every other input at its default and halve the b. See how discriminant responds.

  1. 01New b: -2.5
  2. 02Baseline Discriminant: 1
  3. 03New Discriminant: -17.75
  4. 04Discriminant decreases by 1875% → use this sensitivity to plan for real-world variation.
04 · PATTERN

b doubled

b = -10 (from -5)

Keep every other input at its default and double the b. See how discriminant responds.

  1. 01New b: -10
  2. 02Baseline Discriminant: 1
  3. 03New Discriminant: 76
  4. 04Discriminant increases by 7500% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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