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avatar+193 

What is the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c}$ has a domain of all real numbers?

 Feb 15, 2021
 #1
avatar+116126 
+1

To  have  a domain of all real numbers, the denominator cannot evaluate  to  0 for any real x

 

Therefore.....the  discriminant  must  be  <  0   for  the polynomial in the  denominator

 

So

4^2   - 4 (1)c  <  0

 

16  - 4c  < 0

 

16  <   4c

 

16/4 <   c

 

c  > 4

 

Therefore  c  = 5      is the smallest  integer  value  of  c   that guarantees  a  domain of all reals

 

cool cool cool

 Feb 15, 2021
 #2
avatar+112531 
0

What a clever little Claire.

You get all your homework done for you and you don't have to learn a thing.

 Feb 15, 2021

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