What is real number m -{2} if x axis is tangent at curve y=(m-2)x^2-2x+m-2?

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`{2}=2-[2]`

`m-{2}=m-2+[2]` (i)

since x-axis is tangent to the given curve ,it means slope of the tangent is zero

Given curve is

`y=(m-2)x^2-2x+m-2`

`y'=2(m-2)x-2`

`y'=0 if`

`(m-2)x-1=0`

`(m-2)x=1`

`(m-{2}-[2])x=1`

`m-{2}=3`

**Thus answer is**

m-{2}=3

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