CAPS 2002 Problem 6

Let $n \ge 2$ be a fixed even integer. We consider polynomials of the form $$P(x) = x^n + a_{n-1}x^{n-1} + \cdots + a_1x + 1$$ with real coefficients, having at least one real roots. Find the least possible value of $a^2_1 + a^2_2 + \cdots + a^2_{n-1}$ .