An even polynomial has no real roots

Proved

WorkbookSource.plus_20327

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

lean-workbooksource-checked

Prove that the equation $8x^8 + 3x^6 + 5x^4 + 3x^2 + 10 = 0$ has no real roots.

Source: InternLM Lean-Workbook, record lean_workbook_plus_20327 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_20327 : ¬ (∃ x : ℝ, 8*x^8 + 3*x^6 + 5*x^4 + 3*x^2 + 10 = 0)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_20327; Apache-2.0

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