Question

Equation Is Given In Comments.
1.List The Possible Positive And Negative Real Zeros.
2. List the possible rational roots of the function
3. Between what consecutive Integers could the zeros be found.
4. Find the upper and lower bound of the zeros.

Answer 1

\[f(x) = 4x ^{4} - 5x ^{3} + 6x ^{2} - 8x + 6\]

Answer 2

Where are you at with this?

Answer 3

Well, I could solve all of this with a calculator. But without one, I would be lost as to what to do. Isn't there some q/e or some formula to find the positive and negative roots?

Answer 4

well part one is kind of worded funny in my opinion because there is no way to determine possible irrational roots.

But I suspect they mean integers

I generally ask my students the second question as it takes care of the first ,i.e. integers are ratinal

Answer 5

i am looking through my files now to see if I have the rules for these things written up
(seems I wrote them up a few years bback)

Answer 6

my statement about finding possible irrational roots was false,

you can use the bisection method or the secant line method

though I doubt your question requires that level of depth...

Answer 7

the possible positive and negative rational roots will be of the form c/d where c is a factor of 6 and d is a factor of 4

so factors of 6: 1,2,3,6
factors of 4: 1,2,4

so the possible rational roots are 1,2,3,6,1/2,1/4,3/2,3/4

Answer 8

from these we can answer part 3:
1 and 2

2 and 3

are the pairs here

Answer 9

look up Decartes' Rule of sign for the method for determining the upper and lower bounds

Answer 10

I don't understand how you got part 3. Could you further explain?