Question 51
Let $n \geq 1$ be a positive integer. Find all polynomials of degree $2n$ with real coefficients
$$
P(X) = X^{2n} + (2n-10) X^{2n-1} + a_{2} X^{2n-2} + \ldots + a_{2n-2} X^{2} + (2n-10) X + 1
$$
if it is known that they have positive real roots.
$$
P(X) = X^{2n} + (2n-10) X^{2n-1} + a_{2} X^{2n-2} + \ldots + a_{2n-2} X^{2} + (2n-10) X + 1
$$
if it is known that they have positive real roots.