1.

The number of real solutions of `|2x-x^2-3|=1`is(a) `0`(b) `2`(c) `3`(d) `4`

Answer» `|2x-x^2-3| = 1`
`=>2x-x^2-3 = +-1`
When `2x-x^2-3 = 1`
`=>-x^2+2x-4 = 0`
`=>D = b^2-4ac = 2^2-4(-1)(-4) = 4-16 = -12`
As, `D lt 0`, no real roots are present for this equation.
When `2x-x^2-3 = -1`
`=>-x^2+2x-2 = 0`
`=>D = b^2-4ac = 2^2-4(-1)(-2) = 4-8 = -4`
As, `D lt 0`, no real roots are present for this equation.
So, in both cases, no real solution exists.
So, the correct option is option - `(a)` that is `0`.


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