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Math Help - need help with polyonomial in standard form

  1. #1
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    need help with polyonomial in standard form

    Find a polynomial P(x)=0 in standard form with integer coefficients whose roots are 2/3, -4, 3+i sq root 5.

    Can someone teach me how to start it? thank you!
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  2. #2
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    Quote Originally Posted by Thatoneguy12345 View Post
    Find a polynomial P(x)=0 in standard form with integer coefficients whose roots are 2/3, -4, 3+i sq root 5.

    Can someone teach me how to start it? thank you!
    Think about it this way. If you have a polynomial P(x) = x^2+2x-3 you can factor it to P(x) = (x-1)(x+3). Is it clear that the roots are x=1 and x=-3 ?
    (a root is where a function crosses the x-axis, or equivalently when P(x)=0)

    If this makes sense to you, then the question that you have to answer is simply doing this procedure backwards.

    In other words, P(x) = (x-\frac{2}{3})(x+4)(x-(3+i\sqrt5))
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  3. #3
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    Quote Originally Posted by Thatoneguy12345 View Post
    Find a polynomial P(x)=0 in standard form with integer coefficients whose roots are 2/3, -4, 3+i sq root 5.

    Can someone teach me how to start it? thank you!
    P(x) = k\left(x - \frac{2}{3}\right)(x+4)[x - (3+i\sqrt{5})][x - (3-i\sqrt{5})]

    where k is the constant necessary to make integer coefficients
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