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Math Help - Algebra - Equations

  1. #1
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    Algebra - Equations

    I need help solving these equations;

    6x^3+17x^2-3x-20=0

    And

    X^4-4x^3-7x^2+22x+24=0


    Thank you
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  2. #2
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    In both cases u should have a look to the rational root theorem.
    With it u can find rational roots and then divide the polynomial till u get to an equation that u know how to solve
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  3. #3
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    Yeah.. I'm still kinda lost..
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  4. #4
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    Quote Originally Posted by weasley74 View Post
    I need help solving these equations;

    6x^3+17x^2-3x-20=0

    And

    X^4-4x^3-7x^2+22x+24=0


    Thank you
    Hello,

    as yannick has suggested try to find a rational solution for the first equation.
    By trial and error you'll see that x = 1 is a solution. Thus (x -1) can be factored out of the LHS term of the equation. Use long division:
    Code:
       (6x^3 + 17x^2 - 3x - 20)  (x - 1) = 6x^2 + 23x + 20
       -(6x^3-  6x^2)
      ---------------
               23x^2 - 3x
             -(23x^2 - 23x)
             ---------------
                       20x - 20
                     -(20x - 20)
                    ------------
                              0
    Now the remaining solutions must be in

    6x^2 + 23x + 20 = 0

    With the 2nd equation start with x = -1. Use long division. Try to get another rational solution, use long division again until you have a quadratic equation which can be solved algebraically.
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