lean_workbook_plus_2150

Proved

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

Using the discriminant; $x^2 + 2x + q$ has real solutions for $4-4q \ge 0 \longrightarrow q \le 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_2150  (q : ℝ)
  (f : ℝ → ℝ)
  (h₀ : ∀ x, f x = x^2 + 2 * x + q)
  (h₁ : ∃ x, f x = 0) :
  q ≤ 1   :=  by sorry

Source