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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. For function `f(x) and g(x)` which of the following is true (A) `f(x)g(x)gt0` for all real x (B) `f(x)g(x)lt0` for all real x (C) `f(x)g(x)=0` for some real x (D) `f(x)g(x)=0` for all real x

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