API Tool Calls

Quadratic Formula Calculator

quadratic_solve

Read-onlyIdempotent

Solve ax² + bx + c = 0 from entered coefficients. See real or complex roots, the discriminant and linear or constant cases.

Example tool call

This call uses example arguments supplied in the tool’s input schema.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "a": 1,
      "b": -3,
      "c": 2
    },
    "name": "quadratic_solve"
  }
}

Input Schema

Name	Required	Description
`a`	Yes	Coefficient; zero or absolute magnitude 10^-12 to 10^12.
`b`	Yes	Coefficient; zero or absolute magnitude 10^-12 to 10^12.
`c`	Yes	Coefficient; zero or absolute magnitude 10^-12 to 10^12.

Output Schema

Name	Required	Description	Default
No arguments

Schema Changelog

Changes observed during successful MCP inspections.

AddedOct 4, 2026

TDQS

A4.3/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare read-only, idempotent, non-destructive, and closed-world behavior. The description adds meaningful output-context beyond those annotations by disclosing that results include real or complex roots, the discriminant, and linear/constant cases.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Two compact clauses, front-loaded with the operation and followed by output expectations. No redundant or wasted text.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple, pure-calculation tool with a full output schema and rich annotations, the description supplies all necessary context: input form, output categories, and special cases. Nothing important is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the baseline is 3. The description adds context by placing a, b, and c into the quadratic equation ax² + bx + c = 0, clarifying their roles beyond the schema's repeated generic 'Coefficient' descriptions.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb (solve) and resource (ax² + bx + c = 0) and distinguishes the operation from generic calculators by naming expected outputs: real or complex roots, discriminant, and linear/constant cases. An agent can identify this as the quadratic-equation solver without opening the schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines3/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description implies usage for quadratic equations from coefficients, but it does not explicitly say when to choose this over sibling calculators or when not to use it. Usage is inferable, not guided.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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