Let \(f(x)\) be a monic polynomial with integer coefficients, such that \(f(\alpha )=0=f(2\alpha )\) for some complex number \(\alpha \). Prove that \(f(0)\ne 1\).
Question
Math 6310 • Algebra
Fall 2013 • Question 6
Question
Fall 2013 • Question 6
Let \(f(x)\) be a monic polynomial with integer coefficients, such that \(f(\alpha )=0=f(2\alpha )\) for some complex number \(\alpha \). Prove that \(f(0)\ne 1\).