Question

How do I describe the real zeroes of this function using Descartes's Rule of Signs?

Answer 1

The number of positive roots is the number of changes of signs there are, then decrease by 2 each time and stop when you get to 1 or 0

negative roots, sub every x with -x and reevaluate, count change of signs
decrease by 2 each time and stop when you get to 1 or 0

y=+2x⁵-x⁴-2x³+4x²+x-2
+,-,-,+,+,-
 1    2  3

3 or 1 positive roots

replace x with -x ( baically flip all signs of odd powerd numbers)

y=-2x⁵-x⁴+2x³+4x²-x-2
   -,-,+,+,-,-
     1    2

2 or 0 negative roots



3 or 1 positive roots
2 or 0 negative roots
2nd option is answer