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Math Help - Polynomial Degrees and Zeros

  1. #1
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    Polynomial Degrees and Zeros

    Find a polynomial of degree 3 whose zeros are -3, 3/2 and 2

    a.2x^3-15x-18
    b.2x^2+3x-9
    c.2x^2-7x+6
    d.2x^3-x^2-15x+18
    e.2x^3-7x^2-15x+18

    I know C and B are not options because the degree is not three, but how do I figure out the rest?
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  2. #2
    Junior Member
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    Do you know about the factorial decomposition of polynomials?
    If a polynomial f(x) of degree 3 has 3 real roots, letīs say \alpha, \beta,\gamma then you can write it down as a(x-\alpha)(x-\beta)(x-\gamma) where a is the leading coefficient of your polynomial.
    Obviously, this fact gets generalised for any polynomial of degree n with m roots, n<m.

    That means that you can write your polynomial as a(x+3)(x-3/2)(x-2) since they didnīt tell you explicitly nothing about the leading coefficient of the polynomial, a might be any real number different of zero. So set a=2 since all your options have L.C.=2.
    Apply distributive law (if you have trouble with that tell me and Iīll write it down) and you get option d.
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