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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) < 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

Text Solution

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The correct Answer is:
B
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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]

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Knowledge Check

  • If the roots of cubic ax^(3) + bx^(2) + cx + d = 0 be in G.P., then

    A
    `a^(3)b = c^(3)d`
    B
    `ab^(3) = cd^(3)`
    C
    `c^(3)a = b^(3)d`
    D
    `ca^(3) = bd^(3)`

  • 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

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