Question

PLEASE HELP

The polynomial function f(x) = -x^3 –x^2 + 4x +9 has one positive zero.
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Between what integers does this positive zero occur?

Answer 1

Answer:

(x + 2) ( x - 3) (x - 4) =

(x^2 - x - 6) ( x - 4) =

x^3 - x^2 - 6x

-4x^2 + 4x + 2

_________________

x^3 - 5x^2 - 2x + 24

So we have

1x^3 -5x^2 - 2x + 24

Second one

I'm assuming that this is :

4x^7 -2x^4 + 2x^3 -4x - 9

We have 3 sign changes.....so the number of possible positive roots = 3 or 1

To find the number of possible negative roots, replaxe x with -x and we have

4(-x)^7 - 2(-x)^4 + 2(-x)^3 -4(-x) - 9 =

We have 2 sign changes....so the number of possible negative roots = 2 or 0

-4x^7 -2x^4 - 2x^3 + 4x - 9

Answer 2

(x + 2) ( x - 3) (x - 4) =

(x^2 - x - 6) ( x - 4) =

x^3 - x^2 - 6x

-4x^2 + 4x + 24

_________________

x^3 - 5x^2 - 2x + 24

So we have

1x^3 -5x^2 - 2x + 24

Second one

I'm assuming that this is :

4x^7 -2x^4 + 2x^3 -4x - 9

We have 3 sign changes.....so the number of possible positive roots = 3 or 1

To find the number of possible negative roots, replaxe x with -x and we have

4(-x)^7 - 2(-x)^4 + 2(-x)^3 -4(-x) - 9 =

We have 2 sign changes....so the number of possible negative roots = 2 or 0

-4x^7 -2x^4 - 2x^3 + 4x - 9