# Amazing Polynomials from America

**Algebra**Level pending

There is a smallest positive real number \(a\) such that there exists a positive number \(b\) such that all the roots of the polynomial \(x^3 - ax^2 + bx - a\) are real. In fact, for this value of \(a\), the value of \(b\) is unique. What is the value of \(b\)?