+0  
 
0
35
1
avatar+1123 

Does anybody know how to solve this?

 

Let $f(x) = x^2 + 6x + c$ for all real numbers $x$, where $c$ is some real number.  For what values of $c$ does $f(x) = 0$ have exactly $2$ distinct real roots?

 Aug 10, 2023
 #1
avatar+126978 
+1

This will have two distinct roots when the  discriminant  >  0

 

So

 

6^2  - 4 (1)(c) > 0

 

36 - 4c > 0

 

36 > 4c

 

36/4  > c

 

9 > c

 

It will have two  distinct roots when    c < 9

 

 

cool cool cool

 Aug 10, 2023

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