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

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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=4x7−2x4+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

Aug 23, 2019
edited by jjennylove  Aug 23, 2019

#1
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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   Aug 23, 2019
#2
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for the first one how would insert it in the three slots?

jjennylove  Aug 26, 2019
#3
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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