Question

according to Descartes rule of signs, how many possible negative real roots could the following polynomial function have? f(x)=3x^4-5x^3+5x^2+5x+2

Answer 1

Even powers do not get sign changes, while odd powers do.

f(x)=3x^4-5x^3+5x^2+5x+2
so
f(-x)=3x^4+5x^3+5x^2-5x+2

There is a sign change from 5x^2 to -5x, as well as from -5x to 2. There are either 2 or 0 negative real roots for this function.

Answer 2

awesome thanks :)