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Let a and b be two distinct roots of a p...

Let a and b be two distinct roots of a polynomial equation f(x) =0 Then there exist at least one root lying between a and b of the polynomial equation

A

f(x)

B

f'(x)

C

f''(x)

D

none of these

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The correct Answer is:
B
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Knowledge Check

  • Let a and b be two disiinel roots of a polynomial equation f (x) = 0, Then there exists at least one root lying between a and b of die polynomial equation.

    A
    a) f(x) =0
    B
    b) f'(x) 0
    C
    c) f''(x) =0
    D
    d) None of these

  • The number of real roots of the polynomial equation x^(4)-x^(2)+2x-1=0 is

    A
    0
    B
    2
    C
    3
    D
    4

  • The root of the equation f (x) = 0 in the interval (a,b) is given by

    A
    `(af(b) - bf(a))/(b - a)`
    B
    `(b f(a) - a f(b))/(f(b) - f(a))`
    C
    `(af(b) - bf(a))/(f(b) - f(a))`
    D
    none of these

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    If f(x) is a polynomial such that f(a)f(b)<0, then what is the number of zeros lying between a and b?

    Show that a polynomial of an odd degree has at least one real root.

    Show that between any two roots of e^(x) cos x=1 , there exists at least one root of e^(x) sin x-1=0

    Show that between any two roots of e^(-x)-cos x=0, there exists at least one root of sin x-e^(-x)=0

    Find the roots of the rational polynomial equation (x^2-6x+8)/(x+2)=0 .

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