Problem

Source: Spain Mathematical Olympiad 2020 P1

Tags: algebra, polynomial, arithmetic sequence, Spain



A polynomial $p(x)$ with real coefficients is said to be almeriense if it is of the form: $$ p(x) = x^3+ax^2+bx+a $$ And its three roots are positive real numbers in arithmetic progression. Find all almeriense polynomials such that $p\left(\frac{7}{4}\right) = 0$