A quartic with no real roots

Proved

WorkbookSource.problem_45335

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

lean-workbooksource-checked

Prove that $4x^{4} -2x+c=0$ has no real roots if $c > \frac{3}{4}$ .

Source: InternLM Lean-Workbook, record lean_workbook_45335 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_45335 (c : ℝ) (h : c > 3/4) : ¬ (∃ x, 4*x^4 - 2*x + c = 0)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_45335; Apache-2.0

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