MathDB

1

Part of 2020 Spain Mathematical Olympiad

Problems(1)

Polynomials with roots in arithmetic progression.

Source: Spain Mathematical Olympiad 2020 P1

7/14/2020
A polynomial p(x)p(x) with real coefficients is said to be almeriense if it is of the form:
p(x)=x3+ax2+bx+a 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(74)=0p\left(\frac{7}{4}\right) = 0
algebrapolynomialarithmetic sequenceSpain