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THE FEUTEX TOOLKIT

Quadratic Real Root Solver

Find both real roots and the vertex of a quadratic polynomial from its coefficients.

Math workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaRoot Plus = (-b+sqrt(b**2-4*a*c))/(2*a); Root Minus = (-b-sqrt(b**2-4*a*c))/(2*a); Vertex X = -b/(2*a); Vertex Y = c-b**2/(4*a)
Sources and model references

Worked example

Inputs

Quadratic coefficient
1 coefficient
Linear coefficient
-5 coefficient
Constant
6 coefficient

Expected results

Root Plus
3 number
Root Minus
2 number
Vertex X
2.5 number
Vertex Y
-0.25 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "a": 1,
  "b": -5,
  "c": 6
}

Accuracy and scope

Solves ax²+bx+c=0 over the reals. Cancellation can affect a small root when coefficients have extreme scale differences. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.