Polynomial with positive real roots
Source: Moldova IMO-BMO TST 2003, day 2, problem 1.
August 15, 2008
algebrapolynomialVieta
Problem Statement
Let be a natural number. Determine all the polynomials of degree with real coefficients in the form
P(X)\equal{}X^{2n}\plus{}(2n\minus{}10)X^{2n\minus{}1}\plus{}a_2X^{2n\minus{}2}\plus{}...\plus{}a_{2n\minus{}2}X^2\plus{}(2n\minus{}10)X\plus{}1,
if it is known that all the roots of them are positive reals.
Proposer: Baltag Valeriu