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

Annotations already declare readOnlyHint, destructiveHint=false, and openWorldHint=false, so the safety profile is covered. The description adds two useful facts beyond that: results may be complex, and a must be non-zero. It does not disclose what happens if a=0 is supplied, or how the coefficient path and equation-string path interact.

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

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

Three short sentences, front-loaded with the equation form, followed by result domain and the one hard constraint. No filler and nothing redundant.

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

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

This tool is mathematically self-contained, the schema fully documents all five parameters with examples, an output schema exists so return values need no explanation, and annotations cover the safety profile. The only remaining ambiguity, coefficient-vs-equation precedence, is already documented per-parameter in the schema.

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

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

Schema description coverage is 100% and every parameter carries an inline description plus examples, so the schema does the heavy lifting and baseline 3 applies. The description adds only the a≠0 constraint, which is already stated verbatim in the schema, and says nothing about precedence when both input forms are present.

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

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

States a specific verb and resource ("Solve ax² + bx + c = 0") and names the exact problem class, which is enough to separate it from general solvers like calculator_numerical_solve or calculator_polynomial. It does not explicitly contrast with nearby siblings such as calculator_cubic_equation, calculator_root_finder, or calculator_quadratic_regression, so it stops short of a 5.

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

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

There is no when-to-use guidance, no mention of alternatives, and no exclusion rules. Crucially, the schema allows two input modes (coefficients a/b/c vs. an "equation" string plus "variable"), yet the description never says which mode to prefer or whether both can be mixed, so the agent must guess how to call it.

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