Prove2Me

A quartic with no negative roots

Proved
WorkbookSource.plus_54270

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

lean-workbooksource-checked

Show that the equation x4−x3−6x2−2x+9=0x^4 -x^3-6x^2-2x+9 = 0 cannot have negative roots.

Source: InternLM Lean-Workbook, record lean_workbook_plus_54270 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.plus_54270 : ¬ (∃ x : ℝ, x < 0 ∧ x^4 - x^3 - 6 * x^2 - 2 * x + 9 = 0)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_54270; Apache-2.0

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