RootFinder

Find Roots

Security Level 1 (Enabled)

SindByte tool execution flow: voice command, AI parse, execute, validate, result

Description

Numerically finds the roots (zeros) of functions. Supports several algorithms: Newton-Raphson, bisection, secant method. Ideal for nonlinear equations that cannot be solved analytically.

JSON Parameters

{
  "function": "x^2 - 4",
  "method": "newton",
  "initialGuess": 1.5,
  "tolerance": 1e-7,
  "maxIterations": 100
}

Parameter	Type	Required	Description
`function`	String	Yes	The function as a formula (f(x) = 0)
`method`	String	No	newton, bisection, secant (default: newton)
`initialGuess`	Number	Yes	Starting value for the search
`interval`	Array	For bisection	[a, b] interval with a sign change
`tolerance`	Number	No	Accuracy (default: 1e-7)
`maxIterations`	Number	No	Maximum iterations (default: 100)

Example Usage

API call:

POST /api/v1/tools/rootfinder
Content-Type: application/json

{
  "function": "x^2 - 4",
  "method": "newton",
  "initialGuess": 1.5
}

Examples

Quadratic equation:

{
  "function": "x^2 - 4",
  "method": "newton",
  "initialGuess": 3
}

Trigonometric:

{
  "function": "sin(x) - 0.5",
  "method": "bisection",
  "interval": [0, 2]
}

Cubic:

{
  "function": "x^3 - 2*x^2 - 5",
  "method": "secant",
  "initialGuess": 2
}

Return Values

{
  "root": 2.0,
  "iterations": 5,
  "converged": true,
  "finalError": 4.8e-9,
  "methodUsed": "newton",
  "success": true
}

Field	Type	Description
`root`	Number	Root found
`iterations`	Number	Number of iterations
`converged`	Boolean	Convergence reached
`finalError`	Number	Final error
`methodUsed`	String	Algorithm used
`success`	Boolean	True if successful

Related Tools

Why This Tool Stands Out

Multiple Methods Choose the best algorithm for your function - every method has its strengths!
Fast Newton-Raphson converges quadratically - the solution in just a few iterations!
Results depend on input, configuration and implementation. Verify behavior in your environment; no accuracy, security or performance guarantee is established here.
Transparent Details on iterations and error - full control over the solution process!

Perfect for:

Researchers Solving equations
Engineers Characteristic curves
Students Numerical analysis exercises

Time Savings

No measured time-saving or performance figures are available here. Results depend on the task and environment.

Ready to Get Started?

Find roots numerically and efficiently.

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