Question 151042
To use Descartes rules of signs, look at P(x) and P(-x)
{{{P(x)=-3x^5-7x^3-4x-5}}}
Since there are no sign changes in the coefficients from + to - or vice versa, then there are no positive roots.
{{{P(-x)=-3(-x)^5-7(-x)^3-4(-x)-5}}}
{{{P(-x)=3x^5+7x^3+4x-5}}}
There is one sign change from + to -, there is exactly one negative root.
{{{ graph( 300, 200, -2, 2, -10, 10, -3x^5-7x^3-4x-5) }}}