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Question

Find all values of a for which the inequality (a+4)x22ax+2a6<0 is satisfied for all xR.

A
For all a(,6)
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B
For all a(,6)
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C
For all a(,+)
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D
For all a(6,)
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Solution

The correct option is A For all a(,6)
The inequality (a+4)x22ax+2a6<0 has to be satisfied for all xR. Only possible when, coefficient of x2 and discriminant value are less than zero.
a+4<0 and 4a24(a+4)(2a6)<0
a(,4) and a2+2a24=(a+6)(a4)>0
a(,4) and a(,6)(4,)
a(,6)
Hence, option A.

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