# 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 $$b$$?

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