Cubic Equations

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I have three that I need help with if possible.
1. Solve 2x^3 - 3x^2 = 6x - 9
2. Find all real and imaginary roots of the polynomial equation 3x^4 - x^3 + 4x^2 - 2x - 4=0
3. Find a cubic equation with integral coefficients and roots 3i and -5.

  • Cubic Equations -

    2 x^3 -3 x^2 -6 x + 9 = 0

    (2x^3 - 6x) - (3 x^2-9) = 0

    2x (x^2-3) -3(x^2-3) = 0

    (x^2-3)(2x-3) = 0
    you take it from there.

    2)
    Try x = 1
    3-1+4-2-4 = 0 amazing
    so divide by (x-1)
    (x-1)(3x^3+2x^2+6x+4) = 0
    (x-1)[ 3x(x^2+2) + 2(x^2+2) ]
    you take it from there

    3)
    (x+5)(x-3i)(x+3i)
    if you have 3i, then you must have the complex conjugate -3i

  • Cubic Equations -

    Thanks so much :D

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