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If c gt 0 and ax^2 + 2bx + 3c = 0 does ...

If `c gt 0` and `ax^2 + 2bx + 3c = 0` does not have any real roots then prove that:
(i) `4a-4b + 3c gt 0`,
(ii) `a + 6b + 27c gt 0`,
(iii) `a + 2b + 6c gt 0`

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