Question

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`

Answer 1

As shown in the sign scheme in the figure
`a-1 le -1 " and " a^2+2 ge 3`
or `a le 0 and a^2 ge 1`
`rArr a le -1`