Question

This is really confusing. Thanks for helping.

Use Descartes’s Rule of Signs to describe the real zeroes of the function f(x) = 2x^5 - x^4 -2x^3 + 4x^2 + x - 2.

A. The function has two or zero positive real zeroes and either three or one negative real zeroes.
B. The function has two or zero negative real zeroes and either three or one positive real zeroes.
C. The function has one positive real zeroes and either four or two negative real zeroes.
D. The function has one negative real zeroes and either four or two positive real zeroes.

Answer 1

count change of signs to tell positive roots
then replace x with -x and evaluate, then count change in sign for negative roots


initially
+, -, -, +, +, -
3 changes
3 or 1 positive roots


replacing x with -x
-,-,+,+,-,-
2 changes
2 or 0 negative roots



B is answer