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If a gt 0 and b^(2) - 4 ac = 0 then solv...

If `a gt 0 and b^(2) - 4 ac = 0` then solve `ax^(3) + (a + b) x^(2) + (b + c) x + c gt 0` .

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We must have `ax^(3) + (a + b)x^(2) + (b + c ) x + c gt 0`
`rArr ax^(2) (x-1) + bx (x-1) + c (x + 1) gt 0`
`rArr (x + 1) (ax^(2) + bx + c ) gt 0`
`rArr a(x + 1 ) (x + (b)/(2a))^(2) gt 0 as b^(2) = 4ac`
`rArr x gt -1 and x ne - (b)/(2a)`
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