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Find the largest integer value of $n$ such that $n^2-9n+18$ is negative.
 
 Oct 26, 2014

Best Answer 

 #1
avatar+130511 
+5

n^2 - 9n + 18

We only need to find out where the "zeroes" of this polynomial are.

So setting it to 0 and factoring, we have

(n - 6) (n-3) = 0

So.......n=6 and n=3

Note that when n = 5, the polynomial's value = -2  and when n = 7, the polynomial's value is 4. And for all integers, n > 7, this polynomial is > 0.

So the largest integer that makes this polynomial negative is when n = 5. Note that n = 6 just makes the polynomial = 0, as we found  !!!!!

 

 Oct 26, 2014
 #1
avatar+130511 
+5
Best Answer

n^2 - 9n + 18

We only need to find out where the "zeroes" of this polynomial are.

So setting it to 0 and factoring, we have

(n - 6) (n-3) = 0

So.......n=6 and n=3

Note that when n = 5, the polynomial's value = -2  and when n = 7, the polynomial's value is 4. And for all integers, n > 7, this polynomial is > 0.

So the largest integer that makes this polynomial negative is when n = 5. Note that n = 6 just makes the polynomial = 0, as we found  !!!!!

 

CPhill Oct 26, 2014

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