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Math Help - Finding possible formulas for a polynomial

  1. #1
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    Exclamation Finding possible formulas for a polynomial

    Find possible formulas for polynomials with the given properties.

    a) f has degree ≤2, f(0) = f(1) = f(2) = 1.
    b) f is third degree with f(-3) = 0, f(1) = 0, f(4) = 0 and f(2) = 5.

    For a) I know that x values 0, 1, and 2 have y values of 1. These points should look like their in a straight formation. But how we find the formula for this? And what about b)?

    Please explain and show me the process to solving these problems. Thanks.
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  2. #2
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    Quote Originally Posted by florx View Post
    Find possible formulas for polynomials with the given properties.

    b) f is third degree with f(-3) = 0, f(1) = 0, f(4) = 0 and f(2) = 5.
    hi

    f(x) is a third degree polynomial with integer coefficient . From the factor theorem , -3 , 1 and 4 are zeros of the polynomial .

    f(x)=a(x+3)(x-1)(x-4)

    f(2)=a(2+3)(2-1)(2-4)

    5=-10 a

    a=-1/2

    Therefore , f(x)=-1/2(x+3)(x-1)(x-4)
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  3. #3
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    Quote Originally Posted by florx View Post
    Find possible formulas for polynomials with the given properties.

    a) f has degree ≤2, f(0) = f(1) = f(2) = 1.
    The possible formulas for this is clearly f(x)=1

    If you want to show it mathematically ,

    Assume that f is of degree 2 , f(x)=ax^2+bx+c

    Find f(0) , f(1) and f(2) , all =1 , then you will have a system simultaneous equations , solve it and you will find that a=0 , b=0 and c=1 .
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  4. #4
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    Thank you so much for showing me how to do these problems.

    However can you clarify on how to prove part b)?
    You said show it mathematically, Assume that f is of degree 2 , f(x)=ax^2+bx+c.

    So for f(0) we would do f(0) = a(0)^2 + b(0) + c?
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  5. #5
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    Quote Originally Posted by florx View Post
    Thank you so much for showing me how to do these problems.

    However can you clarify on how to prove part b)?
    You said show it mathematically, Assume that f is of degree 2 , f(x)=ax^2+bx+c.

    So for f(0) we would do f(0) = a(0)^2 + b(0) + c?
    yes and c=1 .
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