Question

What does Descartes's Rule of Signs tell you about the real roots of the polynomial? –2x3 + 3x2 – 5x – 2 = 0 a. There is one positive root and either two or zero negative roots. b. There are either two or zero positive roots, and there are either two or zero negative roots. c. There is one positive root and one negative root. d. There are either two or zero positive roots and one negative root.

Answer 1

The count the number of times the sign changes
that is how many positive roots there are
if you get a number that is ≥2, then count down by 2's ending at 0

sub -x for x and evaluate
count change in sign again
that is how many negative roots there are
if you get a number that is ≥2, then count down by 2's ending at 0


so

-2x^3+3x^2-5x-2=0
-,+,-,-
 1  2 
2 or 0 positive roots


x to -x
2x^3+3x^2+5x-2=0
+,+,+,-
       1
1 negative root



2 or 0 positive roots and 1 negative root


D is answer