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Determine the value of K, such that y = 3x + k intersects the quadratic equation y = 2x^2 - 5x + 3 at exactly one point. 

Please determine algebraicly, and the answer is 5, however, I am looking for the process.

 Dec 9, 2018
 #1
avatar+94501 
+2

y = 2x^2 - 5x + 3    and   y = 3x + k

 

Set these equal

 

2x^2 - 5x + 3 = 3x + k         rearrange as

 

2x^2 - 8x + (3 - k) = 0

 

If this has one solution , then the discriminant = 0.....so

 

(-8)^2 - 4(2)(3-k) = 0

 

64 - 8(3 - k) = 0

 

This will = 0   when k = -5

 

See the graph here, Drazil : https://www.desmos.com/calculator/mujvkyjtsn

[ The tangent point is (2,1) ]

 

 

cool cool cool

 Dec 9, 2018
edited by CPhill  Dec 9, 2018

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