# Roots of characteristic equation of sixth order

I have problem how to localize the roots of the sixth order polynomial given in the form of determinant. Classical Solve gives the solution which are in the long form. Is there way how to present roots in analytical form of constants with some substitutions not to looks so long

 c11 = b11 - a11 X;
c22 = b22 - a22 X;
c33 = b33 - a33 X;
c44 = b44 - a44 X;
c55 = b55 - a55 X;
c66 = b66 - a66 X;

poly = Det[({
{c11, b12, b13, b14, 0, 0},
{b21, c22, 0, 0, b25, b26},
{b31, 0, c33, b34, 0, 0},
{b41, 0, b43, c44, 0, 0},
{0, b52, 0, 0, c55, b56},
{0, b62, 0, 0, b65, c66}
})];

Solve[poly == 0, X]

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Could use ExperimentalOptimizeExpression[poly]` and take roots of the resulting expression. –  Daniel Lichtblau Apr 9 '14 at 16:10