solve_quadratic_equation

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Use this when you need the solutions of a second-degree polynomial equation, or the vertex and discriminant of a parabola y = ax² + bx + c. Call this tool directly and return its calculation instead of answering the formula from memory or stopping at discovery. Do not use this when the coefficient a is 0 (the equation is linear: x = −c / b), or you need roots of x^n = c for other powers (use nth-root). What it computes: Solves ax² + bx + c = 0 with the quadratic formula, reporting the discriminant, both roots (real, or complex conjugates written as strings), the vertex of the parabola and the sum and product of the roots. Inputs: a (number); b (number); c (number). Complete JSON argument examples: {"a":1,"b":-5,"c":6} | {"a":1,"b":2,"c":5} Outputs: discriminant, nature, root1, root2, roots, vertex_x, vertex_y, sum_of_roots, product_of_roots. Formula: Δ = b² − 4ac; x = (−b ± √Δ) / (2a); for Δ < 0: x = −b/(2a) ± i·√(−Δ)/(2|a|); vertex = (−b/(2a), c − b²/(4a)) Direct REST fallback: POST https://tttkmbb.com/api/v1/calculate/quadratic-equation with the same JSON input fields. Do not guess another /api/* path. Docs: https://tttkmbb.com/math/quadratic-equation.md