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Find the largest integer value of n such that n^2-9n+18 is negative.

 Mar 21, 2020
 #1
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0

n = 4  and  n = 5

 Mar 21, 2020
 #2
avatar+1956 
+1

We can factor this into (n-3)(n-6).

 

The possible values of n will be 6.

 

Hope this helped!

 Mar 21, 2020
edited by CalTheGreat  Mar 21, 2020
 #3
avatar+111321 
+1

We want to solve  this  :

 

n^2- 9n  +  18   <  0            factor the left side

 

(n  - 6) ( n - 3)  <  0

 

Note that this will  be true  when  n is on the interval  (3, 6)

 

So.....the greatest integer value of  n that makes the function negative is  n  = 5

 

 

cool cool cool

 Mar 21, 2020
 #4
avatar+1956 
+1

Wait...Chris! I think you meant 6, right?

CalTheGreat  Mar 21, 2020
 #5
avatar+111321 
+1

No....not 6

 

Look at the graph here :  https://www.desmos.com/calculator/b3vbllckme

 

Note that the roots of this polynomial  are  n = 3  and  n  = 6

 

So....at  n =6, the polynomial   = 0 

 

But we need it to  to be  negative......so.....the largest integer value to  make this true is  n   = 5

 

cool cool cool

CPhill  Mar 21, 2020
edited by CPhill  Mar 21, 2020
edited by CPhill  Mar 21, 2020
 #6
avatar+1956 
+2

Oh yeah!!! Thanks for the explanation, Chris. 

 

Me to myself: "I didn't realize that this was a polynomial! Read the question, Cal!" LOL!

 

Anyway, thanks again!

CalTheGreat  Mar 21, 2020
 #7
avatar+111321 
0

LOL!!!!!

 

 

cool cool cool

CPhill  Mar 21, 2020
 #8
avatar+63 
+1

Thank you so much!

smallbrain  Mar 21, 2020

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