What is the polynomial function of least degree whose only zeros are −2 ,3, and 4?

Drag a value to each parenthese to correctly state the function.

f(x)= x3( ) x2 ( ) x ( )

the options are -24 ,-9 ,-5,-2,2,5,9,24

i am unsure on both questions, can someone help me?

2. According to Descartes's rule of sign, how many possible positive and negative roots are there for the equation 0=4x^{7}−2x^{4}+2x3=^{3}−4x−9 ?

Drag the choices to the boxes to correctly complete the table.

Number of possible positive roots Number of possible negative roots

options are 0 , 1 Only, 2 Only , 0 or 2, 3 Only , 1 or 3

jjennylove Aug 23, 2019

#1**+2 **

First one :

(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 =

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

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

CPhill Aug 23, 2019

#3**+1 **

Well....I'm not sure what the slots are supposed to represent...but

If the first slot is the coefficient on x^3....then it would be (1)

Similarly...on x^2 we have (-5)

And on (x) we have (-2)

What reamains unclear is the "slot" for the constant term....this would be (24)

Hope that helps

CPhill
Aug 26, 2019