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What is the sum of all numbers a for which the graph of y=x^2+a and the graph of y=ax intersect one time?

 Apr 20, 2019
edited by Lightning  Apr 20, 2019
 #1
avatar+104962 
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y = x^2 + a

y = ax

 

Set these equal

 

x^2  + a  =  ax

x^2 - ax + a  = 0

 

If they intersect once.....then there is only  one root  which means that the discriminant  = 0

 

a^2  - 4a  =  0      factor

 

a( a - 4)  =  0

 

a  =  0       or     

 

a  = 4 

 

So....the sum is  4

 

cool cool cool

 Apr 20, 2019

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