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Math Help - Solving a cubic equation.

  1. #1
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    Solving a cubic equation.

    Can anyone help me solve this? Thank you so so much!

    16x^3 -48x^2 -9x + 27=0
    Last edited by mr fantastic; July 6th 2010 at 04:35 PM.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    By guessing one root...

    My "guess" is x=3, now you should know how to continue.
    Read here please: Rational Zeros of Polynomials
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  3. #3
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    Assuming you know the factor theorem
    the numbers are big,
    so arrangement could help
    Solving a cubic equation.-untitled.jpg
    so when x=3 , it satisfies the equation, (x-3) is a factor, and other factors can be found by equating coefficients.
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  4. #4
    Senior Member eumyang's Avatar
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    This cubic can be factored by grouping. Look at the first pair of terms and factor out the GCF; then do the same for the last pair.
    \begin{aligned}<br />
16x^3 - 48x^2 - 9x + 27 &= 0 \\<br />
16x^2(x - 3) - 9(x - 3) &= 0\\<br />
(x - 3)(16x^2 -9) &= 0<br />
\end{aligned}<br />
    Can you take it from here? Finish factoring (look at 16x^2 - 9), and set each factor equal to 0.
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  5. #5
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    THANK YOU ALL SO MUCH! This is very helpful!
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