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Let y= mx-2 be the tangent line to y=x^2-4x+2 at x=a.
Then slope,
Hence the equation is y=(2a-4)x-2
Let's find y-coordinate at x=a using tangent line and curve.
Using tangent line y at x=a is (2a-4) a -2
Using given curve y-coordinate at x=a is
Let's equate these 2 y-coordinates,
a=2 or -2.
If a=2,
If a=-2,
Hence m values are 0 and -8.