Question 8
A real-coefficient polynomial $p(x)$ is called *Almerian* if it has the form
$$
p(x) = x^3 + ax^2 + bx + a
$$
and its three roots are positive real numbers in arithmetic progression. Find all Almerian polynomials satisfying $p(7/4)=0$.
$$
p(x) = x^3 + ax^2 + bx + a
$$
and its three roots are positive real numbers in arithmetic progression. Find all Almerian polynomials satisfying $p(7/4)=0$.