Prove that for any value of a, the inequ...

Prove that for any value of a, the inequatiion `(a^(2)+3)x^(2)+(a+2)x-6lt0` is true for atleast one negative `x`.

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We have `(a^(2)-3)x^(2)+(a+2)x-6lt0`

Let `f(x)=(a^(2)+3)x^(2)+(a+2)x-6`
`(a^(2)+3)gt0` and `f(x)lt0`
`:.Dgt0`
`implies(a+2)^(2)+24(a^(2)+3)gt0` is true for all `a epsioonR`

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