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Question

Find all values of a for which the inequality (a3)x22ax+3a6<0 is satisfied for all values of x.

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Solution

(a3)x22ax+3a6<0xϵR
a3<0
a<3
aϵ(,3)
b<0
(2a)24.3(a3)(a2)<0
4a24.3(a25a+6)<0
a23a2+15a18<0
2a215a+18>0
2a212a3a+18>0
(2a3)(a6)>0
aϵ(,32)(6,)
aϵ(,32)

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