Home
Class 12
MATHS
Let f(x)=ax^2+bx+c,a,b,cepsilon R a !=0 ...

Let `f(x)=ax^2+bx+c,a,b,cepsilon R a !=0` such that `f(x)gt0AAxepsilon R` also let `g(x)=f(x)+f\'(x)+f\'\'(x)`. Then (A) `g(x)lt0AAxepsilon R` (B) `g(x)gt0AAxepsilon R` (C) `g(x)=0` has real roots (D) `g(x)=0` has non real complex roots

Promotional Banner

Similar Questions

Explore conceptually related problems

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) gt 0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in

Let f(x) be polynomial function of defree 2 such that f(x)gt0 for all x in R. If g(x)=f(x)+f'(x)+f''(x) for all x, then

Let f(x)=x^2+bx+c and g(x)=af(x)+bf\'(x)+cf\'\'(x). If f(x)gt0AAxepsilonR then the sufficient condition of g(x) to be gt0AAxepsilon R is (A) cgt0 (B) bgt0 (C) blt0 (D) clt0

Q. if f(x) is a quadratic expression such that f(x)>0 AA x epsilon R, and if g(x)=f(x)+f'(x)+f(x), then prove that g(x)>0 x epsilon R. Let f(x)=ax^2+bx+c Given that f(x)>0 so >0, b^2-4ac 0 and discriminant

Suppose that f(0)=0 and f'(0)=2, and let g(x)=f(-x+f(f(x))). The value of g (0) is equal to

Let g'(x)>0 and f'(x)<0AA x in R, then

Let f''(x) gt 0 AA x in R and let g(x)=f(x)+f(2-x) then interval of x for which g(x) is increasing is