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Let f(x) be a quadratic expression which...

Let `f(x)` be a quadratic expression which is positive for all real x and `g(x)=f(x)+f'(x)+f''(x)`.A quadratic expression `f(x)` has same sign as that coefficient of `x^2` for all real`x` if and only if the roots of the corresponding equation `f(x)=0` are imaginary.Which of the following holds true? (A) `g(0)g(1)lt0` (B) `g(0)g(-1)lt0` (C) `g(0)f(1)f(2)gt0` (D) `f(0)f(1)f(2)lt0`

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