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Math Help - Another polynomial problem

  1. #1
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    Another polynomial problem

    Find all the solutions of the equation p(x) = 0 if

    p(x) = 3(x)^4 + 5(x)^3 + 25(x)^2 + 45x - 18

    and 3i is one of the solutions.
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  2. #2
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    Hello, NeedHelp18!

    Find all the solutions of: . 3x^4 + 5x^3 + 25x^2 + 45x - 18 \:=\:0 if 3i is one of the solutions.

    If 3i is a solution, then -3i is also a solution.
    . .
    Complex roots appear in conjugate pairs.

    Then (x-3i)(x+3i) \:=\:x^2+9 is a factor of the polynomial.

    Using long division, we have: . (x^2+9)(3x^2+5x-2) \:=\:0

    . . which factors further: . (x^2+9)(x+2)(3x-1) \:=\:0


    Therefore, the roots are: . 3i,\:-3i,\:-2,\:\tfrac{1}{3}

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