Let `f(x)=a x^2+b x+c` be a quadratic expression having its vertex at (3, -2) and value of `f(0)=10. F in df(x)dot`

Let f(x) be a quadratic expression such that f(-1)+f(2)=0 . If one root of f(x)=0 is 3 , then the other root of f(x)=0 lies in (A) (-oo,-3) (B) (-3,oo) (C) (0,5) (D) (5,oo)

Let f(x) be a quadratic expression such that f(-1)+f(2)=0 . If one root of f(x)=0 is 3 , then the other root of f(x)=0 lies in (A) (-oo,-3) (B) (-3,oo) (C) (0,5) (D) (5,oo)

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

If f(x) is a quadratic expression such that f(1) + f(2) = 0, and -1 is a root of f(x) = 0 , then the other root of f(x) = 0 is :

If f(x) is a quadratic expression such that f(1)+f(2)=0, and -1 is a root of f(x)=0, then the other root of f(x)=0 is :

" Let "f(x)=ax^(2)+bx+c=0" be a quadratic equation and "alpha,beta" are its roots then "f(-x)=0" is an equation whose roots "

If f(x) is a quadratic function such that f(0)=3,f(1)=6 and f(2)=11 , then: f(x)=

Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least value at x =- and the graph of f (x) cuts y-axis at y =2. The value of f (-2) + f(0) + f(1)=