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Math Help - Auxiliary Eq (Dif EQ)

  1. #1
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    Auxiliary Eq (Dif EQ)

    Suppose we are given two roots, m_1 = \frac{-1}{2} and m_2 = 3 + i, of a cubic auxiliary equation which has real coefficients. Determine what the corresponding homogeneous linear Dif EQ is.

    WORK:

    No idea.

    So wouldn't we have Am^3 + Bm^2 + Cm + D = 0, and when we solve that for m we get the two values listed above. Not sure how to do this..
    Last edited by Ideasman; October 4th 2007 at 12:50 PM.
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  2. #2
    Super Member Rebesques's Avatar
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    You can suppose A=1.

    So write (m-m_1)(m-m_2)(m-m_3)=(m+1/2)(m-3-i)(m-m_3) for the auxiliary equation. Since it has real coefficients and a complex root, its conjugate is also a root.
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