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Math Help - 5th-degree polynomial equation

  1. #1
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    5th-degree polynomial equation

    3x^5 + 4x^4 + 6x^3 - 20x^2 - 25x = 0

    by the way, the answers are the following:

    0, -1, 5/3 & -12i


    *** i need a complete solution on how to solve this eqn plzzzz
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  2. #2
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    Quote Originally Posted by fishlord40 View Post
    3x^5 + 4x^4 + 6x^3 - 20x^2 - 25x = 0

    by the way, the answers are the following:

    0, -1, 5/3 & -12i


    *** i need a complete solution on how to solve this eqn plzzzz
    First x=0 is an obvious root so that leaves us with:

    3x^4+4x^3+6x^2-20x-25=0

    The rational roots theorem tells us that if this has any rational roots they are the ratio of a factor of the constant term to a factor of the coefficient of the higest order term, so try: x= \pm 1, \pm 5, \pm 5/3, \pm 25, \pm 25/3. Having found all the rational roots remove the corresponding factors, which will leave you with a quadratic, and on that you use the quadratic formula.

    CB
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  3. #3
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    Quote Originally Posted by fishlord40 View Post
    3x^5 + 4x^4 + 6x^3 - 20x^2 - 25x = 0

    by the way, the answers are the following:

    0, -1, 5/3 & -12i


    *** i need a complete solution on how to solve this eqn plzzzz
    HI

    3x^5 + 4x^4 + 6x^3 - 20x^2 - 25x = 0

    x(3x^4+4x^3+6x^2-20x-25)=0

    It's obvious here that x=0

    Now you can use the rational root test to find the possible zeros for the polynomial inside the bracket

    THe possible ones are \pm \frac{1,5,25}{1,3}

    \pm 1, \pm \frac{1}{3} ,

    \pm 5 , \pm \frac{5}{3} , \pm 25 ,

    \pm \frac{25}{3}

    whichever roots which give you 0 when you substitute them into the equation would be the zeros . In this case , they would be -1 and 5/3 .

    3x^4+4x^3+6x^2-20x-25=(x+1)(3x-5)(ax^2+bx+c)

    Use the long division to find the quadratic , and solve it where it would give you complex roots .
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  4. #4
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    Talking

    Quote Originally Posted by fishlord40 View Post
    i need a complete solution on how to solve this eqn
    To learn the process (so you can do these types of exercises on your own on the test), try here.
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