Question

5. What does Descartes's Rule of Signs tell you about the real roots of the polynomial?

–2x3 + 3x2 – 5x – 2 = 0 (1 point)
There is one positive root and either 2 or 0 negative roots.
There are either 2 or 0 positive roots and there are either 2 or 0 negative roots.
There is one positive root and one negative root.
There are either 2 or 0 positive roots and one negative root.

Answer 1

count the number of changes in sign for positive roots, keep minusing 2 until you reach 0 or 1

negative: replace x with -x and evaluate
count changes in sign


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


replace with -x
2x^3+3x^2+5x-2
+,+,+,-
       1
1 change in sign
1 negative




last option