Suppose that `f(x)` isa quadratic expresson positive for all real `xdot` If `g(x)=f(x)+f^(prime)(x)+f^(x),` then for any real `x(w h e r ef^(prime)(x)a n df^(x)` represent 1st and 2nd derivative, respectively). `g(x)<0` b. `g(x)>0` c. `g(x)=0` d. `g(x)geq0`

Let f(x) be a quadratic expression possible for all real x. If g(x)=f(x)-f'(x)+f''(x), then for any real x

Let f(x) be a quadratic expression which is positive for all ral x and g(x) = f(x) + f'(x) + f''(x), then for any real x,

Let f (x) be a quadratic expratic expressinon which is positive for all real values of x, If g(x)=f(x)+f'(x)+f''(x), then for any real x

If f(x) is a quadratic expression such that f(x)gt 0 AA x in R , and if g(x)=f(x)+f'(x)+f''(x) , then prove that g(x)gt 0 AA x in R .

Let f(x) be a polynomial of degree two which is positive for all x in R. If g(x)=f(x)+f(x)+f'(x)+xf''(x)+x^(2)f^(iv)(x) then for any real x,prove that g(x)>0

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