Question

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Please help!!!!!
Using complete sentences, describe how you would analyze the zeros of the polynomial function f(x) = –3x5 – 8x4 +25x3 – 8x2 +x – 19 using Descartes’ Rule of Signs. (2 points)

Be sure to provide the answer in your explanation.

Answer 1

@whpalmer4 @satellite73

Answer 2

now this is completely different, because it is asking for descartes rule of sign, not "possible rational zeros"

Answer 3

Yes

Answer 4

\[ f(x) = –3x^5 – 8x^4 +25x^3 – 8x2 +x – 19 \] as 4 changes in sign

Answer 5

from \(-8\) to \(+25\)
from \(+25\) to \(-8\)
from \(-8\) to \(1\) and
from \(1\) to \(-19\)

Answer 6

and you count down by 2's so there are either
4 positive zeros
2 positive zeros
no positive zeros

Answer 7

then do the same computation for \(f(-x)\)

Answer 8

\[f(x) = –3x^5 – 8x^4 +25x^3 – 8x^2 +x – 19\]
\[f(-x)=3x^5-4x^4-25x^3-8x^2-x-19\]

Answer 9

again count the changes in sign to find the possible number of negative zeros

Answer 10

Thank you just one more question .

Answer 11

in this case there is only 1 change in sign, from \(3\) to \(-8\) so there must be one negative zero