Home
Class 12
MATHS
Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d...

Given P(x) `=x^(4) +ax^(3) +bx^(2) +cx +d` such that x=0 is the only real root of P'(x) =0 . If P(-1) lt P(1),` then in the interval `[-1,1]`

A

`P(-1)` is the minimum and P(1) is the maximum of P

B

`P(-1)` is not minimum but P(1) is the maximum of P

C

`P(-1)` is the minimum but P(1) is not the maximum of P

D

Neither `P(-1)` is the minimum nor P(1) is the maximum of P.

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise CHAPTER TEST (1)|12 Videos

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

If f(x) = x^4 + ax^3 + bx^2 + cx = d such that x = 0 is the only real root of P'(x) = 0. If P(-1) lt P(1) then in the interval [-1,1]

Given P(x)""=""x^4+""a x^3+""c x""+""d such that x""=""0 is the only real root of P '(x)""=""0.""If""P(1)""<""P(1) , then in the interval [1,""1] . (1) P(1) is the minimum and P(1) is the maximum of P (2) P(1) is not minimum but P(1) is the maximum of P (3) P(1) is the minimum but P(1) is not the maximum of P (4) neither P(1) is the minimum nor P(1) is the maximum of P

Knowledge Check

  • Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only real root of P'(x) =0 . If P(-1) < P(1), then in the interval [-1,1]

    A
    P(-1) is the minimum and P(1) is the maximum of P
    B
    P(-1) is not minimum but P (1)is the maximum of P
    C
    P(-1) is the minimum and P(1) is not the maximum of P
    D
    neither P(-1) is the minimum nor P(1) is the maximum of P

  • 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

    A
    `-d//a`
    B
    `d//a`
    C
    `a//d`
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    Let P(x) = x^4 + ax^3 + bx^2 + cx + d, where a, b, c, d in RR .Suppose P(0) = 6, P(1)=7, P(2) = 8 and P(3)=9, then find the value of P(4).

    If P(x)=x^(4)+ax^(3)+bx^(2)+cx+d,P(1)=P2=P(3)=0 then find P(4)

    Let P(x)=x^(4)+ax^(3)+bx^(2)+cx+d, where a ,b,c,d in R. Suppose P(0)=6,P(1)=7,P(2)=8 and P(3)=9 , then find the value of P(4)

    Let P(x)=x^(4)+ax^(3)+bx^(2)+cx+d, where a,b,c,d in RR . Suppose P(0)=6,P(1)=7,P(2)=8 and P(3)=9, then find the value of P(4)

    In the given figure graph of y = P(x) = ax^(5) + bx^(4) + cx^(3) + dx^(2) + ex + f , is given. The minimum number of real roots of equation (P''(x))^(2) + P'(x).P'''(x) = 0 , is

    x^2 + x + 1 is a factor of ax^(3) + bx^2 + cx + d = 0 , then the real root of above equation is ( a,b,c,d in R )

    Home
    Profile