Use Descartes' Rule of Signs to determine the possible number of positive and nega- tive zeros of $f ( x ) = x ^ { 5 } + 2 x$
A) 1 positive real; 3 negative reals or 1 negative real
B) no positive reals; no negative reals
C) 1 positive real; 5 negative reals or 3 negative reals or 1 negative real
D) 5 positive reals or 3 positive reals or 1 positive real; no negative reals
E) 3 positive reals or 1 positive real; 3 negative reals or 1 negative real

Question

Quizplus · Accepted Answer

The polynomial $f(x) = x^5 + 2x$ has no sign changes, so there are no positive or negative real zeros according to Descartes' Rule of Signs.

Use Descartes' Rule of Signs to Determine the Possible Number f(x)=x5+2xf ( x ) = x ^ { 5 } + 2 xf(x)=x5+2x

Use Descartes' Rule of Signs to Determine the Possible Number $f ( x ) = x ^ { 5 } + 2 x$