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Find the greatest integer value of b for which the expression

 

(9x^3+4x^2+11x+7)/(x^2+bx+18)

 

has a domain of all real numbers.

 Mar 12, 2021
 #1
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We just need  to make sure   that  x^2  + bx   + 18    does  not  =  0

 

In other words,  we  need to have  the  discriminant  of  this  function be <  0

 

So

 

b^2  - 4 (1) (18)  <  0

 

b^2   - 72  <  0

 

b^2  <  72

 

This will  be  true  for  the  integer values  on    [ -8, 8  ]  

 

So  b  =  8  is the largest integer value of  b that will  give us a domain of all reals

 

 

cool cool cool

 Mar 12, 2021

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