Ensure your polynomial's terms are written in descending order. This one is.
Multiply each odd-order term by -1. (to the fifth, third and so on). Note: the constant term is the zero order term and zero is even.
Count the number of sign changes from term to term. You will have at most this number of negative real zeros. It could be less counting by twos. So if you have 3 sign changes after the -1 multiplications, then you have 3 or 1 real negative zeros. If you have 2 sign changes then you have 2 or 0 real negative zeros. And if you have 1 sign change, then you have exactly 1 real negative zero.
John
My calculator said it, I believe it, that settles it
