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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?

I was told the answer is not 6.

 Mar 4, 2020

Best Answer 

 #1
avatar+21874 
+1

To find where they intersect, set the two equations equal to each other:  x2 + a  =  ax  and solve:

--->      x2 + a  =  ax      --->     x2 - ax + a  =  0

 

Using the quadratic formula:  x  =  [ a +/- sqrt( (-a)2 - 4·1·a } / ( 2·1)    

--->     x  =  [ a +/- sqrt( a2 - 4a ) ] / 2

 

If they intersect in only one point,  a2 - 4a  must equal zero.

 

If     a2 - 4a  =  0     --->     a(a - 4)  =  0

either     a = 0    or    a = 4

 

The sum of these two possibilities is  0 + 4  =  4

 Mar 4, 2020
 #1
avatar+21874 
+1
Best Answer

To find where they intersect, set the two equations equal to each other:  x2 + a  =  ax  and solve:

--->      x2 + a  =  ax      --->     x2 - ax + a  =  0

 

Using the quadratic formula:  x  =  [ a +/- sqrt( (-a)2 - 4·1·a } / ( 2·1)    

--->     x  =  [ a +/- sqrt( a2 - 4a ) ] / 2

 

If they intersect in only one point,  a2 - 4a  must equal zero.

 

If     a2 - 4a  =  0     --->     a(a - 4)  =  0

either     a = 0    or    a = 4

 

The sum of these two possibilities is  0 + 4  =  4

geno3141 Mar 4, 2020

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