Home
Class 12
MATHS
Let f(x) = ax^2 + bx +C,a,b,c in R.It ...

Let `f(x) = ax^2 + bx +C,a,b,c in R`.It is given `|f(x)|<=1,|x|<=1` The possible value of `|a + c|` ,if `8/3a^2+2b^2` is maximum, is given by

A

1

B

0

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|3 Videos
  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|27 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|24 Videos

Similar Questions

Explore conceptually related problems

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

Let f(x)=ax^(2)+bx+c AA a,b,c in R,a!=0 satisfying f(1)+f(2)=0. Then,the quadratic equation f(x)=0 must have :

Knowledge Check

  • Let f(x) = ax^(2) + bx + c, a, b, c, in R and equation f(x) - x = 0 has imaginary roots alpha, beta . If r, s be the roots of f(f(x)) - x = 0 , then |(2,alpha,delta),(beta,0,alpha),(gamma,beta,1)| is

    A
    0
    B
    purely real
    C
    purely imaginary
    D
    none of these
  • Let f(x) = ax^(2) + bx + c ,where a, b, c in R . Suppose |f (x) |le 1 AA x in [0,1] , then |a| cannot exceed

    A
    5
    B
    6
    C
    7
    D
    8
  • If f(x) = ax^(2) + bx + c find f^(1) (1) .

    A
    `a+2b`
    B
    `2a -b`
    C
    `a-2b`
    D
    `2a +b`
  • Similar Questions

    Explore conceptually related problems

    Let f(x)=ax^(2)+bx+a,b,c in R. If f(x) takes real values for real values of x and non- real values for non-real values of x ,then a=0 b.b=0 c.c=0 d.nothing can be said about a,b,c.

    Let f(x)=ax^(2)+bx+c where ab,c varepsilon Randa!=0lt is given that f(5)=-3f(2) and 3 is a root of f(x)= Othen:

    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

    If f(x) = a + bx + cx^2 where a, b, c in R then int_o ^1 f(x)dx

    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)=