Question

Can someone check my answers for these three problems?
1. Use Descarte'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. (MY CHOICE)
d. The function has one negative real zeroes and either four or two positive real zeroes.

Answer 1

Are you familiar with Descartes rule of signs?
`The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number. Multiple roots of the same value are counted separately.` (ref. Wiki)

How many changes of sign have you counted?

Examples:
http://www.purplemath.com/modules/drofsign.htm

Answer 2

I counted 3 sign changes.

Answer 3

So according to the Descartes rule, up to how many possible positive roots can there be?

Answer 4

There can be up to two or zero real positive zeroes. Right?

Answer 5

Did you read this part?
`...then the number of positive roots of the polynomial is either equal to the number of sign differences...`

Answer 6

Oh... so it would have three or one positive real zeroes.

Answer 7

Exactly!

Answer 8

Okay thank you so much