Determining a quadratic coefficient from a value

Proved

WorkbookSource.problem_35786

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $c\in\mathbb R$ and $f:\mathbb R\to\mathbb R$ satisfy $f(x)=x^2-5x+3c$ for every real $x$ . If $f(3)=-12$ , then

c=-2.

Source: InternLM Lean-Workbook, record lean_workbook_35786 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_35786  (c : ℝ)
  (f : ℝ → ℝ)
  (h₀ : ∀ x, f x = x^2 - 5 * x + 3 * c)
  (h₁ : f 3 = -12) :
  c = -2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_35786; Apache-2.0

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