+0

0
77
8
+63

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

Mar 21, 2020

#1
0

n = 4  and  n = 5

Mar 21, 2020
#2
+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
+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

Mar 21, 2020
#4
+1956
+1

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

CalTheGreat  Mar 21, 2020
#5
+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

CPhill  Mar 21, 2020
edited by CPhill  Mar 21, 2020
edited by CPhill  Mar 21, 2020
#6
+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
+111321
0

LOL!!!!!

CPhill  Mar 21, 2020
#8
+63
+1

Thank you so much!

smallbrain  Mar 21, 2020