calculus

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Form a polynomial f(x) with real coeffiecients having the given degree and zeros.

degree 4, zeros 3, multiplicity 2; 6i
f(x)=a()

Can someone show how to do this. I have tried and do not have a clue. I am lost!!! So, please show work.

  • calculus -

    by the time you get to calculus, you should know how to use the roots to form a polynomial. If you tried, you should show what you have tried, and where you got stuck.

    If a is a root of f(x)=0, (x-a) is a factor of f(x).

    Since complex roots come in pairs, -6i is also a root, so

    f(x) = (x-3)(x-3)(x-6i)(x+6i)
    = (x-3)^2 (x^2+36)

    saying you do not have a clue indicates either
    a) you have woefully neglected your studies, or
    b) you are just lazy and want someone else to do your work, or
    (c) both of the above.

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