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Math Help - Polynomials

  1. #1
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    Polynomials

    Suppose p is a polynomial of degree 3 with three zeros at x=1, x=2, and x=3. Find p if p(x) evaluated at 5 is 48.
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  2. #2
    Junior Member PaulAdrienMauriceDirac's Avatar
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    Re: Polynomials

    Since we know that 1,2,3 are roots, we can write that:

    P(x)=a(x-1)(x-2)(x-3)

    P(5)=a(5-1)(5-2)(5-3)=24a=48 -> a=2.

    Now distribute 2 in P(x)=a(x-1)(x-2)(x-3):

    P(x)=2(x-1)(x-2)(x-3)=(2x-2)(x-2)(x-3)=

    =(2x^2-6x+4)(x-3)=2x^3-12x^2+22x-12.

    So P(x)=2x^3-12x^2+22x-12.

    I hope you understand now.
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  3. #3
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    Re: Polynomials

    Thank you so much! Huge help!!
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