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Math Help - Polynomial

  1. #1
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    Question Polynomial

    How to solve this in simple way ...?

    What is the value of x ?
    x3 + x2 + x + 1 = 0
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  2. #2
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    Re: Polynomial

    Yes you can factorise by grouping...

    $\displaystyle \begin{align*} x^3 + x^2 + x + 1 &= 0 \\ x^3 + x + x^2 + 1 &= 0 \\ x\left( x^2 + 1 \right) + 1 \left( x^2 + 1 \right) &= 0 \\ \left( x^2 + 1 \right) \left( x + 1 \right) &= 0 \\ x^2 + 1 = 0 \textrm{ or } x + 1 &= 0 \end{align*}$

    The first equation doesn't have any real solutions (if you want complex solutions they're $\displaystyle \begin{align*} x = \pm \mathrm{i }\end{align*}$) and the second equation has solution x = -1.
    Thanks from AlvaJr
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