Find the values of m for which the lines y=mx-2 are tangents to the curve with equation y=x^2-4x+2

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.