+0  
 
0
160
2
avatar+604 

For what real values of $c$ is $9x^2 + 16x + c$ the square of a binomial? If you find more than one, then list your values in increasing order, separated by commas.

gueesstt  Apr 22, 2018
 #1
avatar+87301 
+1

9x^2  + 16x + c

 

A perfect square binomial will have one root

 

So...in the quadratic formula, we will have one root when the discriminant, b^2  - 4ac, equals 0....so....

 

16^2  - 4* 9 * c   =  0

 

256   - 36c  = 0       add 36 c to both sides

 

256  =  36c        divide both sides by 36

 

64/9   =  c

 

 

cool cool cool

CPhill  Apr 22, 2018
 #2
avatar+604 
+1

Thank you!

gueesstt  Apr 22, 2018

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