Question 5
Let $f(x)=x^2-\alpha x+1$, where $\alpha\in\mathbb R$.
(a) For $\alpha=\sqrt{15}/2$, express $f$ as the quotient of two polynomials with nonnegative coefficients.
(b) Find all real $\alpha$ for which such a representation exists.
(a) For $\alpha=\sqrt{15}/2$, express $f$ as the quotient of two polynomials with nonnegative coefficients.
(b) Find all real $\alpha$ for which such a representation exists.