lean_workbook_plus_70352

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that if $a + b + c \ge 0, a - b + c \ge 0, a - c \ge 0$ , then the absolute values of both roots of the polynomial $P(x) = ax^2 + bx + c$ with $a > 0$ are less than or equal to $1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_70352 (a b c : ℝ) (ha : a > 0) (hab : a + b + c ≥ 0) (hac : a - c ≥ 0) (hbc : a - b + c ≥ 0) : ∀ x : ℝ, a * x ^ 2 + b * x + c = 0 → abs x ≤ 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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