List the signs of the coefficients of each term. That is, the signs of the numbers in front of the x^n and the constant. The max number of positive real roots is either the number of sign changes, or the number of sign changes decreased by a multiple of 2.

Make sure the polynomial is written in decreasing order of exponents. That is ^n , ^(n-1), ^(n-2)...
x^4 + x^3 – 7x – 1 has coefficients 1, 1 -7 -1. The signs are:

+, +, -, - There is one sign change (from + to -), therefore the maximum number of positive real roots is 1 or -1 0r -3 or...

There can't be a negative number of positive real roots. So the answer is 1.

This is Descartes Rule of Signs.