The Invariant Root

Algebra Level 5

Consider all fifth degree polynomials \(p(x) \) with integer coefficients, such that \(p(x) \) has at least 1 integral root, \( p(2) = 13 \) and \( p(10 ) = 5 \).

There is a complex number \( \alpha \) such that \( p( \alpha ) = 0 \) for all such polynomials. Find \( | \alpha | \).

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.