descartes rule of signs to determine the possible number of positive and negative real zeros of: p(x)=x^4-40x+39

Answer 1

Number of positive roots of a polynomial P is the number of sign changes of P(X) or an even integer less.

Number of negative roots of P is a number of sign changes of P(-x) or an even integer less.

P(x) leaves p(x) unchanged with two sign changes, so there are 2 or 0 positive roots

P(-x) leaves p(x) with no sign changes, so there are 0 negative roots.