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.

Drazil Dec 9, 2018

#1**+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) ]

CPhill Dec 9, 2018