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Question

Consider the equation x2+x+a9<0. The values of the real parameter a so that the given equation has at least one positive solution are

A
(,374)
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B
(,)
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C
(3,)
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D
(,9)
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Solution

The correct option is D (,9)
Given,
x2+x+a9<0
(x+12)2+a374<0
has atleast one positive solution
i.e.,atleast one solution is such that x>0
x+12>12
(x+12)2>14
(x+12)214>0
=>(x+12)2+a374<0<(x+12)214
=>(x+12)2+a374<(x+12)214
a<9
=>a(,9)
Hence, option D is correct.

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