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
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
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
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