Free · Algebra and geometric models
Recognize Signed Perfect-Square Quadratics
Check a quadratic discriminant and obtain coefficient magnitudes for a signed square representation.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
The polynomial 4x²+12x+9 has zero discriminant and equals (2x+3)².
b²−4ac=0 identifies a signed quadratic square
Worked example
Enter these known values and leave the other values blank.
- a
- 4
- b
- 12
- c
- 9
- Result
- The displayed coefficient magnitudes describe the quadratic.
- Explanation
- The displayed coefficient magnitudes describe the quadratic. a abs = 4.
- Explanation
- The displayed coefficient magnitudes describe the quadratic. b abs = 12.
- Explanation
- The displayed coefficient magnitudes describe the quadratic. c abs = 9.
- Explanation
- The displayed coefficient magnitudes describe the quadratic.
- Explanation
- The displayed coefficient magnitudes describe the quadratic. b abs = 12.
- Explanation
- The displayed coefficient magnitudes describe the quadratic. a abs = 4.
- Explanation
- The displayed coefficient magnitudes describe the quadratic. c abs = 9.
- Explanation
- The displayed coefficient magnitudes describe the quadratic. delta = 0.
- Explanation
- The discriminant is zero: this is a signed perfect square.
- Explanation
- The discriminant is zero: this is a signed perfect square.
- Explanation
- The discriminant is zero: this is a signed perfect square. a abs = 4.
- Explanation
- The discriminant is zero: this is a signed perfect square. b abs = 12.
- Explanation
- The discriminant is zero: this is a signed perfect square. c abs = 9.
- Explanation
- The discriminant is zero: this is a signed perfect square. p = 2. q = 3.
Assumptions and limitations
- The quadratic coefficient is nonzero. Coefficients may be signed.
- A zero discriminant yields a repeated real root; negative leading coefficient gives the negative of a square.
Common questions
What must I enter?
Choose the mode when available and enter its independent known quantities. Leave an unknown editable quantity empty to use a supported inverse.
How should I use the result?
Interpret the numbers within the stated mathematical assumptions. Available unit selectors convert quantities; display rounding does not replace the internal calculation.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.
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