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

Text Solution

AI Generated Solution

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) 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

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , 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

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

Let g(x)gt0andf'(x)lt0,AAx in R, then show g(f(x+1))ltg(f(x-1)) f(g(x+1))ltf(g(x-1))

Let g'(x)gt 0 and f'(x) lt 0 AA x in R , then

Let f(x)=x^(2)+ax+b , where a, b in R . If f(x)=0 has all its roots imaginary, then the roots of f(x)+f'(x)+f''(x)=0 are

Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5)=-3f(2) and that 3 is a root of f(x)=0. Then find the other of f(x)=0.