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Math Help - Finding a degree 3 polynomial w/ specified zeros...

  1. #1
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    Finding a degree 3 polynomial w/ specified zeros...

    Find a degree 3 polynomial with zeros -2, 1, and 5 going through the point [0, -3].

    This is what I have so far:

    y=ax^3 + bx^2 + cx + d

    0=-8a + 4b - 2c + d
    0= a + b + c + d
    0= 125a + 25b + 5c + d
    -3= 0a + 0b + 0c + d

    d= -3

    So how do I solve this system now?

    Any help is greatly appreciated.
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  2. #2
    MHF Contributor red_dog's Avatar
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    Another approach:

    p(x)=a(x+2)(x-1)(x-5)

    p(0)=-3\Rightarrow 10a=-3\Rightarrow a=-\frac{3}{10}

    Now you can expand the polynomial.
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  3. #3
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    How did you get 10a = -3?

    Nevermind. Thank you for your help
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