Solve `x^2-x-2 gt 0.`

Options

A. `x in (- oo, -1 ) cup (2, oo)`
B. `x in ( oo, 2 )`
C. `x !in (- oo, -1 ) cup (2, oo)`
D. `x !in ( oo, 2 )`

Answer

A

Explanation

`x^2-x-2 gt 0.`
or `( x-2)(x+1) gt 0 `
Now `x^2-x- 2=0 rArr x=-1,2`
On the number lilne (x- axis) mark x= -1 and x =2
Now when `x gt 2,x+1 gt 0 " and "x-2 gt 0 `
`rArr (x+1)(x-2) lt 0`
When `-1 lt x lt 2 ,x+1 gt 0 " but " x-2 lt 0`
`rArr (x+1 )(x-2) lt 0`
When `x gt -1 , x+1 lt 0 and x-2 lt 0 `
`rArr (x+1)(x-2) gt 0 `
Hence sing scheme of `x^2- x -2`is
From the figure `x^2- x - 2 gt 0, x in (- oo , -1 ) cup (2.oo)`