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Last updated: July 31, 2026

Generic Rectangle Calculator

Dharmendra Singh - Creator

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Balram Rajput
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Formula

Find p,q with p+q=b and p×q=a×c; roots from quadratic formula and discriminant

Where:

  • a=a coefficient
  • b=b coefficient
  • c=c constant
Generic Rectangle (Box Method)A 2x2 grid representing the area model used to factor a quadratic, with ax squared in the top-left, the split terms px and qx in the other corners, and c in the bottom-right.ax²qxpxcfactor 1factor 2Rulep·q = a·cp + q = b
Split the bx term into px and qx so that p·q equals a·c, then read the factors from each row and column.

Worked Examples

Factorable quadratic

Analyze x²-5x+6.

  1. 1ac=6 and p+q=-5 -> p=-2, q=-3
  2. 2Discriminant = 25-24=1
  3. 3Roots are 3 and 2
Final Answer: p=-2, q=-3, root1=3, root2=2, discriminant=1, isFactorable=true

Non-factorable over integers

Analyze x²+x+1.

  1. 1No integer p,q with pq=1 and p+q=1
  2. 2Discriminant = 1-4=-3
  3. 3No real roots
Final Answer: p=0, q=0, root1=0, root2=0, discriminant=-3, isFactorable=false

Leading coefficient not 1

Analyze 2x²+7x+3.

  1. 1ac=6 and p+q=7 -> p=1, q=6
  2. 2Discriminant = 49-24=25
  3. 3Roots = -0.5 and -3
Final Answer: p=1, q=6, root1=-0.5, root2=-3, discriminant=25, isFactorable=true

Introduction

The generic rectangle (area model) helps split middle terms for quadratic factoring while also exposing discriminant and roots.

Formula and Method

Generic Rectangle Calculator applies Find p,q with p+q=b and p×q=a×c; roots from quadratic formula and discriminant and returns deterministic outputs from validated inputs.

  • Validate each required input

  • Apply the stated formula

  • Round numeric outputs where needed

  • Return safe defaults when validation fails

Input Fields

Use these keys exactly as defined in calculation.ts.

  1. 1

    a: a coefficient

  2. 2

    b: b coefficient

  3. 3

    c: c constant

Output Fields

These values map directly to calculation.ts return keys.

  1. 1

    p: One split value with p+q=b and pq=ac

  2. 2

    q: Other split value

  3. 3

    root1: First real root when available

  4. 4

    root2: Second real root when available

  5. 5

    discriminant: b²-4ac value

  6. 6

    isFactorable: String flag true/false for integer-style split

Validation Rules

a, b, c must be finite and a cannot be zero.

  • Finite numeric values are required

  • Domain restrictions are enforced before solving

  • Invalid input returns default-safe outputs

  • Check examples to confirm expected behavior

How to Use This Calculator

Enter inputs, run the calculation, and read the primary output first.

  • Enter all required values

  • Click calculate

  • Review primary output first

  • Use supporting outputs for interpretation

Practical Uses

This calculator is useful for study, verification, and fast applied math checks.

  • Factoring trinomials

  • Quadratic root analysis

  • Teaching area-model factoring

  • Discriminant interpretation

FAQs

What does the Generic Rectangle Calculator compute?

It computes Split Term p and supporting outputs from your inputs.

Which inputs are required?

Required inputs are: a coefficient, b coefficient, c constant.

How are invalid inputs handled?

When validation fails, the calculator returns safe default values and does not attempt invalid math.

Are results rounded?

Yes. Numeric outputs are rounded inside calculation.ts (typically to 6 decimal places).

Can I use negative or decimal values?

Finite real coefficients are accepted when a ≠ 0.

How should I verify my answer?

Use the worked examples and compare each output key with your manual steps.

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