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.
+23246 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
+23246 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
