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Been here for 6 hours and still didn't get anything:(

 

1.  Consider the polynomial function. 

 

f(x)= x^4 − 2x^3 + 11x^2 + 5x +6

Which statement correctly describes the number of possible positive zeros and the number of possible negative zeros?

a. The number of positive zeros is either 3 or 1. The number of negative zeros is either 2 or 0.

b. The number of positive zeros is either 2 or 0. The number of negative zeros is either 2 or 0.

c. The number of positive zeros is 1. The number of negative zeros is either 3 or 1.

d. The number of positive zeros is either 3 or 1. The number of negative zeros is 1.

 

2. Consider the polynomial function.

 

 

f(x)= x^3(x−2)^2(x+5)

Which statements correctly describes the behavior of the graph of the function at its zeros?

a. The graph of the function crosses through the x-axis at 0 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at −5  and crosses straight through the x-axis at 2.

b. The graph of the function crosses through the x-axis at 2 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at 0 and crosses straight through the x-axis at −5 .

c. The graph of the function crosses through the x-axis at 0 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at 2 and crosses straight through the x-axis at −5

d. The graph of the function crosses through the x-axis at 0 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at −2  and crosses straight through the x-axis at 5.

 Jan 17, 2020
 #1
avatar+18295 
+2

1.  Looking at the coefficients:  +1, -2, +11, +5, +6, there are two changes of signs; thus, only (b) has a chance of being correct.

 

2.  (c) is correct.  

 Jan 17, 2020
 #2
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+1

Thank you so, so much!

Guest Jan 18, 2020

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