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

Annotations already declare readOnlyHint=true, idempotentHint=true, and destructiveHint=false, so the safety profile is covered and the description does not repeat it. The description does add useful behavior (cost of 1 credit, return of roots) but is internally ambiguous: it promises 'real and complex roots' yet also says it 'indicates if no real solutions exist', leaving unclear whether complex roots are actually returned or replaced by a no-solution message.

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?

Two tight sentences plus a cost tag; the operation and formula are front-loaded and nothing is padded. The only efficiency cost is the mild redundancy between the stated purpose and the return sentence, which repeats the 'roots' idea with a conflicting caveat.

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?

For a three-coefficient pure function whose annotations already cover safety, the description gives the operation, the domain, and a rough sense of the return. The remaining gap—no output schema and no statement of how complex roots are shaped (object, string, or flag)—is minor but real for an agent parsing the result.

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 each coefficient is documented there, including the non-zero constraint on 'a', so the schema does the heavy lifting. The description adds only the conventional ax² + bx + c framing, which is helpful context but no meaning beyond the schema, and says nothing about why the schema permits string inputs.

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 plus the exact computation domain: 'Computes the real and complex roots of a quadratic equation ax² + bx + c = 0 using the quadratic formula.' This clearly separates it from generic siblings like calculate, average, or is_perfect_square without opening any schema.

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?

Usage is strongly implied by the mathematical scope (only quadratics, only root-finding), but there is no explicit when-to-use or when-not guidance and no named alternative among the many math siblings. An agent can infer applicability from the formula stated, which is the minimum-viable bar.

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