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Find the set of all possible real value of a such that the inequality `(x-(a-1))(x-(a^2+2))<0` holds for all `x in (-1,3)dot`

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Find the set of all possible real value of a such that the inequality `(x-(a-1))(x-(a^2+2))<0` holds for all `x in (-1,3)dot`<br>A. `(0, 1)`
B. `(infty, -2]`
C. `(-infty, - 1)`
D. `(1, infty)`
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Correct Answer - 2
We have,
` a - 1 le - 1 `
and ` a^(2) + 2 ge 3 `
`a le 0 and a^(2) ge 1`
Hence, a ` le - 1`
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