Question

How do I analyze the zeros of the polynomial function f(x) = 7x5 + 15x4 - x3 + 4x2 - 6x - 11 using Descartes' Rule of Signs?

Answer 1

Look for how many times the sign changes from positive to negative or vice versa. Then find f(-x) and do the same.

Answer 2

I'm not sure what it means by "analyze the zeros"...

Answer 3

That's what threw me off, how do I analyze a zero?

Answer 4

I think it just means find all possibilities. Do it the same way I did that last one with descartes rule of signs.

Answer 5

om, so q is the factors of 7, and p is the factors of 11, right?

Answer 6

*oh

Answer 7

No, descartes rule of signs only looks at the function
f(x) = 7x5 + 15x4 - x3 + 4x2 - 6x - 11
and how many times the sign changes from positive to negative... changes from + to - or vice versa three times. So three possible positive real zeros, or one.

Then find f(-x) (see the last question where i showed it) and find how many times the sign changes from + to -

see this one http://openstudy.com/study#/updates/5120c370e4b06821731cd90f

Answer 8

so, there are 3 times it changes from + to -, so 3 positive zeroes, and the sign changes from - to + 2 times, so 2 negative zeroes, right?

Answer 9

The change in sign is either + to -, or - to +. You have to count how many changes for f(x), then count how many for f(-x) (see the link above).

And it can be an even number less than the possible amount, so here there's three possible positive zeros, or one possible positive zero.

f(-x) = -7x5 + 15x4 + x3 + 4x2 + 6x - 11
So two possible negative zeros, or zero negative zeros.

There'll be 5 zeros total since it's degree 5, so the possible combos of zeros are:
3 pos., 2 neg.
1 pos, 2 neg, 2 complex
3 pos, 0 neg, 2 complex
1 pos, 0 neg, 4 complex

And i think that's all of them.

Answer 10

ok

Answer 11

Thanks!