Question 171
Consider the following polynomial
$$
f(x) = x^2 - \alpha x + 1
$$
with $\alpha \in \mathbb{R}$.
a) For $\alpha = \frac{\sqrt{15}}{2}$, express $f(x)$ as the quotient of two polynomials with non-negative coefficients.
b) Find all values of $\alpha$ such that $f(x)$ can be written as the quotient of two polynomials with non-negative coefficients.
$$
f(x) = x^2 - \alpha x + 1
$$
with $\alpha \in \mathbb{R}$.
a) For $\alpha = \frac{\sqrt{15}}{2}$, express $f(x)$ as the quotient of two polynomials with non-negative coefficients.
b) Find all values of $\alpha$ such that $f(x)$ can be written as the quotient of two polynomials with non-negative coefficients.