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Math Help - polynomial

  1. #1
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    polynomial

    Suppose you know that 3 is one of the zeros of the polynomial p=x^3-x^2-11x+15.

    Find all the other zeros.

    Briefly explain why you know that you have found all of the zeros.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by gumi View Post
    Suppose you know that 3 is one of the zeros of the polynomial p=x^3-x^2-11x+15.

    Find all the other zeros.

    Briefly explain why you know that you have found all of the zeros.
    There are 3 zeros for this polynomial....we know this because it is of degree three...and since x=3 is a zero we know that x-3 is a factor...so your p can be factored into something like p=(x-3)(ax^2+bx+c)...to obtain the quadratic synthetically divide
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  3. #3
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    Hello, gumi!

    Suppose you know that 3 is one of the zeros of: p(x) \:=\:x^3-x^2-11x+15

    Find all the other zeros.
    Briefly explain why you know that you have found all of the zeros.

    If x = 3 is a zero of p(x), then (x-3) is a factor of p(x).

    We find that: . p(x) \;=\;(x-3)(x^2+2x-5)

    . . And the other two zeros of p(x) are: . \boxed{x \:=\:-1 \pm\sqrt{6}}


    A cubic polynomial can have at most three zeros.

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