Verified answer

Descartes' rule is based on the number of sign changes in the non-zero coefficients when the powers of x are in descending order. There are 3 such changes (-2 to +3, +3 to -6, and -6 to +1).

The number of positive real zeroes is either equal to the number of sign changes, or less than that by a multiple of 2. That means there can either be 3 positive real zeroes or 1 positive real zero.

To get the number of negative real zeroes, you have to reverse the sign on the odd powers of x (or equivalently, look at P(-x) instead of P(x)). x^5 is the only odd power of x with a non-zero coefficient in our polynomial, so we're looking at the coefficients 2 3 -6 1. There are two sign changes, so there can either be 2 negative real zeroes or no negative real zeroes.