Answer
number of positive real zeros: $2,0$
number of negative real zeros: $0$
Work Step by Step
Step 1. Given the function
$f(x)=3x^4-2x^3-8x+5$
we can identify that there are 2 sign changes and based on Descartes’s Rule of Signs, we can determine the possible number of positive real zeros to be $2,0$
Step 2. Examine
$f(-x)=3(-x)^4-2(-x)^3-8(-x)+5=3x^4+2x^3+8x+5$
we can identify that there are 0 sign changes and based on Descartes’s Rule of Signs, we can determine the possible number of negative real zeros to be $0$
