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Math Help - finding rational zeros of a function

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    finding rational zeros of a function

    ok the problem states find all rational zeros of the function f(x)= 2x^4-15x^3+23x^2+15x-25
    i got:

    P:-1,+1
    q: -1,+1,-5,+5,+25,-25,

    there are additional factors for the constant, what are they and how do i go about finding them? i dont want pts taken off from my exam by not finding ALL the factors.

    and when i solve this problem, should i use the quadratic function or should i continue using synthetic division until its completely factorized? i got the answer, i just continued using synthetic division, i see that u can also use the quadratic function, question is does it matter what i use?

    thanks!
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    Re: finding rational zeros of a function

    Quote Originally Posted by noork85 View Post
    ok the problem states find all rational zeros of the function f(x)= 2x^4-15x^3+23x^2+15x-25
    i got:

    P:-1,+1
    q: -1,+1,-5,+5,+25,-25,

    there are additional factors for the constant, what are they and how do i go about finding them? i dont want pts taken off from my exam by not finding ALL the factors.

    and when i solve this problem, should i use the quadratic function or should i continue using synthetic division until its completely factorized? i got the answer, i just continued using synthetic division, i see that u can also use the quadratic function, question is does it matter what i use?

    thanks!
    if p indicates factors of the leading coefficient, then you forgot the factors of 2 ...

    once synthetic division gets you down to a quadratic, then use the method you find easiest for determining the remaining zero(s).
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    Re: finding rational zeros of a function

    i thought u only factor the constant, that being 25.
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    Re: finding rational zeros of a function

    ok so

    factors of constant are:+-1,+-5,+-25
    factors of coefficient are:+-1,+-2
    possible zeros are obtained by dividing the factors of constant by factors of coefficient? and they are,
    +-,+-5,+-25,+-,1/2,+-5/2,+-25/2

    is there an easier way to obtain the possible zeros when u have alot to divide?
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    Re: finding rational zeros of a function

    Quote Originally Posted by noork85 View Post
    ok so

    factors of constant are:+-1,+-5,+-25
    factors of coefficient are:+-1,+-2
    possible zeros are obtained by dividing the factors of constant by factors of coefficient? and they are,
    +-,+-5,+-25,+-,1/2,+-5/2,+-25/2

    is there an easier way to obtain the possible zeros when u have alot to divide?
    I always start with the easy candidates ... \pm 1 ... I note that x = 1 is a zero right off

    you can also use the intermediate value theorem to find intervals that have zeros.
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    Re: finding rational zeros of a function

    can u please demonstrate that with this example?
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    Re: finding rational zeros of a function

    Quote Originally Posted by noork85 View Post
    can u please demonstrate that with this example?
    f(x)= 2x^4-15x^3+23x^2+15x-25

    f(2) = 9 , f(3) = -16

    since f(x) is a continuous polynomial function, this tells you you have a zero between x = 2 and x = 3 ... try x = 5/2
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