Home
Class 12
MATHS
Suppose a, b, c,d be non-zero real numb...

Suppose a, b, c,d be non-zero real number and `ab gt 0`, and `int_(0)^(1)"("1+e^(x^(2))")"(ax^(3)+bx^(2)+cx+d)dx=int_(0)^(2)"("1+e^(x^(2))")"`
`(ax^(3)+bx^(2)+cx+d)dx=0`
The equation `ax^(3)+bx^(2)+cx+d=0` has

A

three positive roots

B

three negative roots

C

two positive and one negative roots

D

one positive & two negative roots

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-I ) Previous Year|4 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year|8 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 3 ( Subjective )|26 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

Similar Questions

Explore conceptually related problems

Suppose a, b, c,d be non-zero real number and ab gt 0 , and int_(0)^(1)"("1+e^(x^(2))")"(ax^(3)+bx^(2)+cx+d)dx=int_(0)^(2)"("1+e^(x^(2))")" (ax^(3)+bx^(2)+cx+d)dx=0 {:(" Column- I"," Column-II"),("(A) The function " f(x)=(x)/((1+x^(2))),"(P)" (-oo,-1)),(" decreases in the interval ",),("(B) The function "f(x)=tan^(-1)x-x,"(Q)"(-oo,0)),("(C) The function ","(R)"(0,oo)),(f(x)=x-e^(x)+tan((2x)/(7)),"(S)"(1,oo)),("increases in the interval","(T)"(-oo,oo)):}

int(ax^3+bx^2+cx+d)dx

Knowledge Check

  • Suppose a, b, c,d be non-zero real number and ab gt 0 , and int_(0)^(1)"("1+e^(x^(2))")"(ax^(3)+bx^(2)+cx+d)dx=int_(0)^(2)"("1+e^(x^(2))")" (ax^(3)+bx^(2)+cx+d)dx=0 Rolle's theorem can be applied for ax^(3)+bx^(2)+cx+d=0 the interval

    A
    [0, 1]
    B
    [0, 2]
    C
    [1, 2]
    D
    None of these

  • Suppose a, b, c,d be non-zero real number and ab gt 0 , and int_(0)^(1)"("1+e^(x^(2))")"(ax^(3)+bx^(2)+cx+d)dx=int_(0)^(2)"("1+e^(x^(2))")" (ax^(3)+bx^(2)+cx+d)dx=0 If f(x)=int f(x) dx= int_(0)^(1)f(x)dx=int_(0)^(2)f(x)dx=0 then in which of the following can Rolle's theorem can be applied for F(x), where f(x)=(1+e^(x^(2)))(ax^(3)+bx^(2)+cx+d)

    A
    [0, 1]
    B
    [0, 2]
    C
    [1 , 2]
    D
    all of these

  • Let a, b and c be non - zero real numbers such that int _(0)^(3) (3ax ^(2) + 2bx +c) dx = int _(1)^(3) (3ax^(2) + 2bx +c) dx , then

    A
    `a+b+c= 3`
    B
    `a+b+c=1`
    C
    `a+b+c=0`
    D
    `a+b+c=2`

    • Similar Questions

    Explore conceptually related problems

    Let a,b,c be non-zero real numbers such that int_(0)^(1)(1+cos^(8)x)(ax^(2)+bx+c)dx=int_(0)^(2)(1+cos^(8)x)(ax^(2)+bx+c)dx then the quadratic equation ax^(2)+bx+c=0 has -

    If (12a+5b)/(15)=-((c+d))/(4), then the equation ax^(4)+bx^(2)+cx+d=0 has

    Let a, b, c be non zero numbers such that int_(0)^(3)sqrt(x^(2)+x+1)(ax^(2)+bx+c)dx=int_(0)^(5)sqrt(1+x^(2)+x)(ax^(2)+bx+c)dx . Then the quadratic equation ax^(2)+bx+c=0 has

    If x^(2)+x+1 is a factor of ax^(3)+bx^(2)+cx+d , then the real root of ax^(3)+bx^(2)+cx+d=0 is

    int_(0)^(1)[(d)/(dx)(sqrt(1+x^(3)))]dx=

    Home
    Profile