{
  "title": "Quadratic formula calculator",
  "human_url": "https://happytails.ai/en/calculators/quadratic-formula/",
  "agent_url": "https://happytails.ai/agents/en/calculators/quadratic-formula/",
  "language": "en",
  "markdown_url": "https://happytails.ai/en/calculators/quadratic-formula.md",
  "content": "Quadratic formula calculator\nSolve a quadratic, including complex and repeated roots.\nHow can we improve this tool?\nReport a problem or share an idea.\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\nHow to use Quadratic formula calculator\nEnter the values you want to calculate and choose the relevant units or settings.\nThe result updates as you type. Adjust the available settings if needed.\nReview the result, then use Copy result or a download link when available.\nUseful next steps\nScientific calculator\nSlope calculator\nPythagorean theorem calculator\nHow to use it\nWrite the equation as ax² + bx + c = 0, then enter its three coefficients. The discriminant b² - 4ac tells you whether the roots are real, repeated or complex.\nA worked example\nFor x² - 5x + 6 = 0, enter 1, -5 and 6. The roots are 2 and 3. For x² + 1 = 0, the roots are i and -i.\nWhat to know\nIf a is zero, the tool handles the remaining linear equation. All-zero coefficients mean infinitely many solutions. Very large or ill-conditioned inputs remain subject to floating-point rounding.",
  "content_format": "text/plain",
  "visibility": "public",
  "links": [
    {
      "name": "Scientific calculator",
      "url": "https://happytails.ai/en/calculators/scientific-calculator/"
    },
    {
      "name": "Slope calculator",
      "url": "https://happytails.ai/en/calculators/slope-calculator/"
    },
    {
      "name": "Pythagorean theorem calculator",
      "url": "https://happytails.ai/en/calculators/pythagorean-theorem/"
    }
  ],
  "tool": {
    "id": "quadratic-formula",
    "category": "calculators",
    "built": true,
    "requirements": "If a is zero, the tool handles the remaining linear equation. All-zero coefficients mean infinitely many solutions. Very large or ill-conditioned inputs remain subject to floating-point rounding.",
    "implementation": {
      "fields": [
        {
          "key": "a",
          "label": "Coefficient a",
          "value": 1,
          "type": "number",
          "min": -1e+100,
          "max": 1e+100,
          "step": "any"
        },
        {
          "key": "b",
          "label": "Coefficient b",
          "value": -5,
          "type": "number",
          "min": -1e+100,
          "max": 1e+100,
          "step": "any"
        },
        {
          "key": "c",
          "label": "Coefficient c",
          "value": 6,
          "type": "number",
          "min": -1e+100,
          "max": 1e+100,
          "step": "any"
        }
      ],
      "input": false,
      "live": true,
      "presentation": "metrics",
      "note": "Solves ax² + bx + c = 0, including complex roots and linear cases. Uses a numerically stable real-root calculation. Floating-point results are rounded to 12 significant digits.",
      "experience": {
        "automatic": true,
        "single": false,
        "inputMaxLength": 1000000,
        "inputMode": "text",
        "label": "Your text",
        "placeholder": "Type or paste your input…",
        "help": "Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.",
        "action": null
      },
      "mode": "automatic",
      "interactive": false
    },
    "execution": "Browser interface",
    "api": null,
    "browser_agent": {
      "supported": true,
      "name": "run_current_tool",
      "discovery": "WebMCP on the human page in a supporting browser",
      "verification": "See audit/API-AUDIT.md; availability is not verification"
    }
  },
  "markdown": "# Quadratic formula calculator\n\n- Human page: https://happytails.ai/en/calculators/quadratic-formula/\n- Markdown: https://happytails.ai/en/calculators/quadratic-formula.md\n- Structured JSON: https://happytails.ai/agents/en/calculators/quadratic-formula/index.json\n- Visibility: public\n\n## Tool capabilities\n\n| Property | Value |\n| --- | --- |\n| Tool ID | `quadratic-formula` |\n| Category | calculators |\n| Implementation | Registered implementation. Registration alone is not a production-quality guarantee. |\n| Browser execution | Automatic updates after valid input or file selection. |\n| Browser processing | Browser; see tool notes for network behavior. |\n| HTTP API | Not callable through HTTP. |\n| Browser-agent interface | run_current_tool |\n\n### Implementation notes\n\nSolves ax² + bx + c = 0, including complex roots and linear cases. Uses a numerically stable real-root calculation. Floating-point results are rounded to 12 significant digits.\n\n### Inputs and settings\n\nNo free-text input is required. Use the file inputs and/or settings below.\n\n| Setting | Meaning | Control type | Default | Constraints |\n| --- | --- | --- | --- | --- |\n| `a` | Coefficient a | number | 1 | min=-1e+100 max=1e+100 step=any |\n| `b` | Coefficient b | number | -5 | min=-1e+100 max=1e+100 step=any |\n| `c` | Coefficient c | number | 6 | min=-1e+100 max=1e+100 step=any |\n\n### Browser-agent workflow\n\n1. Open the human page in a browser that supports WebMCP.\n2. Discover the interface exposed by that page; use its actual schema.\n3. Select files on the page first when the tool requires files.\n4. Call `run_current_tool` with valid input and settings.\n5. Inspect the returned result or error and the displayed output. Retrieve files from the displayed download links.\n\nCalls do not automatically copy or download results. Browser permissions still apply. Interface availability alone is not proof of successful execution.\n\n### Planning specification\n\nIf a is zero, the tool handles the remaining linear equation. All-zero coefficients mean infinitely many solutions. Very large or ill-conditioned inputs remain subject to floating-point rounding.\n\nThis describes intended requirements. Use the implementation notes, interface schema and observed output to determine current support.\n\n### Complete machine-readable capability record\n\n```json\n{\n  \"id\": \"quadratic-formula\",\n  \"category\": \"calculators\",\n  \"built\": true,\n  \"requirements\": \"If a is zero, the tool handles the remaining linear equation. All-zero coefficients mean infinitely many solutions. Very large or ill-conditioned inputs remain subject to floating-point rounding.\",\n  \"implementation\": {\n    \"fields\": [\n      {\n        \"key\": \"a\",\n        \"label\": \"Coefficient a\",\n        \"value\": 1,\n        \"type\": \"number\",\n        \"min\": -1e+100,\n        \"max\": 1e+100,\n        \"step\": \"any\"\n      },\n      {\n        \"key\": \"b\",\n        \"label\": \"Coefficient b\",\n        \"value\": -5,\n        \"type\": \"number\",\n        \"min\": -1e+100,\n        \"max\": 1e+100,\n        \"step\": \"any\"\n      },\n      {\n        \"key\": \"c\",\n        \"label\": \"Coefficient c\",\n        \"value\": 6,\n        \"type\": \"number\",\n        \"min\": -1e+100,\n        \"max\": 1e+100,\n        \"step\": \"any\"\n      }\n    ],\n    \"input\": false,\n    \"live\": true,\n    \"presentation\": \"metrics\",\n    \"note\": \"Solves ax² + bx + c = 0, including complex roots and linear cases. Uses a numerically stable real-root calculation. Floating-point results are rounded to 12 significant digits.\",\n    \"experience\": {\n      \"automatic\": true,\n      \"single\": false,\n      \"inputMaxLength\": 1000000,\n      \"inputMode\": \"text\",\n      \"label\": \"Your text\",\n      \"placeholder\": \"Type or paste your input…\",\n      \"help\": \"Change the input or settings to update your result. Results update as you type. Up to 1,000,000 characters.\",\n      \"action\": null\n    },\n    \"mode\": \"automatic\",\n    \"interactive\": false\n  },\n  \"execution\": \"Browser interface\",\n  \"api\": null,\n  \"browser_agent\": {\n    \"supported\": true,\n    \"name\": \"run_current_tool\",\n    \"discovery\": \"WebMCP on the human page in a supporting browser\",\n    \"verification\": \"See audit/API-AUDIT.md; availability is not verification\"\n  }\n}\n```\n\n## Page guide\n\nSolve a quadratic, including complex and repeated roots.\n\nHow can we improve this tool?\n\nReport a problem or share an idea.\n\nPlease leave out private information. Your message and the tool name go to our team via PostHog.\n\n### How to use Quadratic formula calculator\n\n1. Enter the values you want to calculate and choose the relevant units or settings.\n2. The result updates as you type. Adjust the available settings if needed.\n3. Review the result, then use Copy result or a download link when available.\n\n## Useful next steps\n\n- [Scientific calculator](https://happytails.ai/en/calculators/scientific-calculator/) ([Markdown](https://happytails.ai/en/calculators/scientific-calculator.md))\n\n- [Slope calculator](https://happytails.ai/en/calculators/slope-calculator/) ([Markdown](https://happytails.ai/en/calculators/slope-calculator.md))\n\n- [Pythagorean theorem calculator](https://happytails.ai/en/calculators/pythagorean-theorem/) ([Markdown](https://happytails.ai/en/calculators/pythagorean-theorem.md))\n\n## How to use it\n\nWrite the equation as ax² + bx + c = 0, then enter its three coefficients. The discriminant b² - 4ac tells you whether the roots are real, repeated or complex.\n\n### A worked example\n\nFor x² - 5x + 6 = 0, enter 1, -5 and 6. The roots are 2 and 3. For x² + 1 = 0, the roots are i and -i.\n\n### What to know\n\nIf a is zero, the tool handles the remaining linear equation. All-zero coefficients mean infinitely many solutions. Very large or ill-conditioned inputs remain subject to floating-point rounding.\n"
}