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Math Help - Zeros and Multiplicity

  1. #1
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    Zeros and Multiplicity

    For each polynomial function, state the zeros and the multiplicity.

    (1) f(x) = 4(x + 4) [(x + 3)]^2

    (2) f(x) = 4x(x^2 - 3)
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    Hello,
    Quote Originally Posted by magentarita View Post
    For each polynomial function, state the zeros and the multiplicity.

    (1) f(x) = 4(x + 4) [(x + 3)]^2

    (2) f(x) = 4x(x^2 - 3)
    A number a is a zero of a polynomial if (x-a) divides the polynomial.
    A number a is a zero of a polynomial, with multiplicity b if (x-a)^b divides the polynomial.

    It should be enough to do the exercise
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    Can you....

    Quote Originally Posted by Moo View Post
    Hello,

    A number a is a zero of a polynomial if (x-a) divides the polynomial.
    A number a is a zero of a polynomial, with multiplicity b if (x-a)^b divides the polynomial.

    It should be enough to do the exercise
    Can you do the first one and I'll take it from there?
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    Moo
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    Quote Originally Posted by magentarita View Post
    Can you do the first one and I'll take it from there?
    Ok, but I would like you to show me how you do the second one then

    f(x)=4(x+4)(x+3)^2

    You can see that (x+4) divides f(x). More exactly, if x=-4, you can see that x+4=0, that is to say f(-4)=0. Thus -4 is a zero.

    What for x+3 ? If x=-3, x+3=0. Then f(-3)=0. -3 is a zero.

    Now, what are their multiplicity ?
    A zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial.
    The factor x+3 appears twice since it is (x+3)^2=(x+3)(x+3). Its multiplicity is 2.

    The factor (x+4) appears only once. Its multiplicity is 1.
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    Based on...........

    Quote Originally Posted by Moo View Post
    Ok, but I would like you to show me how you do the second one then

    f(x)=4(x+4)(x+3)^2

    You can see that (x+4) divides f(x). More exactly, if x=-4, you can see that x+4=0, that is to say f(-4)=0. Thus -4 is a zero.

    What for x+3 ? If x=-3, x+3=0. Then f(-3)=0. -3 is a zero.

    Now, what are their multiplicity ?

    The factor x+3 appears twice since it is (x+3)^2=(x+3)(x+3). Its multiplicity is 2.

    The factor (x+4) appears only once. Its multiplicity is 1.
    Based on this reply, I should be able to find the zeros of similar polynomials.

    Thanks
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    great

    Quote Originally Posted by Moo View Post
    Hello,

    A number a is a zero of a polynomial if (x-a) divides the polynomial.
    A number a is a zero of a polynomial, with multiplicity b if (x-a)^b divides the polynomial.

    It should be enough to do the exercise
    What a great set of tips.
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  7. #7
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    Thanks Moo!
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