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Prove that the equation a3 – 4.x + 2 = 0 has three irrational solutions. Hin %3D but just show that they exist and are not rational.

Prove that the equation a3 – 4.x + 2 = 0 has three irrational solutions. Hin %3D but just show that they exist and are not rational.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Title: Irrational Roots of Polynomial Equations** **Problem Statement:** Prove that the equation \(x^3 - 4x + 2 = 0\) has three irrational solutions. **Hint:** Do not find the solutions but just show that they exist and are not rational. **Explanation:** The problem involves showing that a cubic polynomial equation has three irrational roots. Instead of solving for the roots, use the properties of polynomials and the rational root theorem to deduce the nature of these roots.
Transcribed Image Text:**Title: Irrational Roots of Polynomial Equations** **Problem Statement:** Prove that the equation \(x^3 - 4x + 2 = 0\) has three irrational solutions. **Hint:** Do not find the solutions but just show that they exist and are not rational. **Explanation:** The problem involves showing that a cubic polynomial equation has three irrational roots. Instead of solving for the roots, use the properties of polynomials and the rational root theorem to deduce the nature of these roots.
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