Home
Class 12
MATHS
Let f(x)=x^2+b x+c ,w h e r eb ,c in Rd...

Let `f(x)=x^2+b x+c ,w h e r eb ,c in Rdot` If `f(x)` is a factor of both `x^4+6x^2+25a n d3x^4+4x^4+28 x+5` , then the least value of `f(x)` is `2` b. `3` c. `5//2` d. `4`

A

2

B

3

C

`(5)/(2)`

D

4

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|20 Videos

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise COMPREHENSIONS - I|3 Videos

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|28 Videos

  • PROGRESSION & SERIES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • SET, RELATION & FUNCTION

    FIITJEE|Exercise Exercise 3|8 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^(2)+bx+c , where b, c inR If f (x) is a factor of both x^(4)+6x^(2)+25 and 3x^(4)+4x^(2)+28x+5. then the least value of f (x) is

Let f(x)=x^(2)+bx+c, where b,c in R. If f(x) is a factor of both x^(4)+6x^(2)+25 and 3x^(4)+4x^(4)+28x+5 then the least value of f(x) is 2 b.3 c.5/2 d.4

Knowledge Check

  • If f(x) = 4x^(4) + x^(2) + 5b and f(1) = f(-1) , then what is the value of b ?

    A
    `b ne 0`
    B
    `b in R`
    C
    no value of `b` is possible
    D
    none of these

  • Let f(x)=x^(4)-4x^(3)+4x^(2)+c, c in R . Then

    A
    f(x) has infinitely many zeros in (1, 2) for all c
    B
    f(x) has exactly one zero in (1, 2) if `-1 lt c lt 0`
    C
    f(x) has double zeros in (1, 2) if `-1 lt c lt 0`
    D
    whatever be the value of c,f(x) has no zero in (1,2)

  • Let f(x) =(x -2) (x^(4) -4x^(3) + 6x^(2) - 4x +1) then value of local minimum of f is

    A
    `-2//3`
    B
    `-(4//5)^(4)`
    C
    `-4^(4)//5^(5)`
    D
    `-(4//5)^(5)`

    • Similar Questions

    Explore conceptually related problems

    Let p(x)=x^(2)+bx+c, where b and c are integers.If p(x) is a factor of both x^(4)+6x^(2)+25 and 3x^(4)+4x^(2)+28x+5 find the value of p(1).

    let P(x)=x^(2)+bx+c, wherer b and c are interger.if P(x) is a factor of both x^(4)+6x^(2)+25 and 3x^(2)+4x^(2)+28x+5 find value of p(1)

    Let P(x)=x^2+b x+cw h e r eba n dc are integer. If P(x) is a factor of both x^4+6x^2+25a n d3x^4+4x^2+28 x+5,t h e n a.P(x)=0 has imaginary roots b.P(x)=0 has roots of opposite c.P(1)=4 d .P(1)=6

    Show that (x+2) is a factor of f(x) = x^(3) + 5=4x^(2) + x - 6.

    If int(5x^(4)+4x^(5))/((x^(5)+x+1)^(2))dx=f(x)+C , then the value of (1)/(f(1)) is

    Home
    Profile