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Math Help - Contructing Polynomial Functions

  1. #1
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    Contructing Polynomial Functions

    I have to make a polynomial function that uses these:

    Third-degree, with zeros of -3, -1, and 2, and passes through the point (4, 7)

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  2. #2
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    Hello !

    Quote Originally Posted by mankvill View Post
    I have to make a polynomial function that uses these:

    Third-degree, with zeros of -3, -1, and 2, and passes through the point (4, 7)

    If -3, -1 and 2 are zeros of the polynomial P(x), then x-(-3)=x+3, x+1 and x-2 divide P(x).

    But (x+3)(x+1)(x-2) is already a polynomial of degree 3. So P(x) is just proportional to (x+3)(x+1)(x-2).

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

    But we know that P(4)=7. Substituting, you can get a
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    ...I'm confused. What is the answer, then?

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    Quote Originally Posted by mankvill View Post
    ...I'm confused. What is the answer, then?

    Because (4,7) belongs to the polynomial function, 7=P(4)=a(4+3)(4+1)(4-2)=a*7*5*2=70a


    ----> a=\frac 1{10}


    P(x)=\frac 1{10}(x+3)(x+1)(x-2)

    Develop to get the complete polynomial
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  5. #5
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    x^3/10 + x^2/5 - x/2 - 3/5

    Is this correct?

    edit: i don't know how to make a nominator and denominator, obviously
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    Quote Originally Posted by mankvill View Post
    x^3/10 + x^2/5 - x/2 - 3/5

    Is this correct?
    Yes
    And when checking, we get P(-3)=P(-1)=P(2)=0 and P(4)=7, which is exactly what we wanted

    edit: i don't know how to make a nominator and denominator, obviously
    \frac{numerator}{denominator}
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