# Math Help - Auxiliary Eq (Dif EQ)

1. ## 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..

2. 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.