If $a, b, c \ \epsilon \ R$, find the number of real roots of the equation given by $ \Delta = 0 $, where $\Delta =\begin{vmatrix} x & c & -b\ -c & x & a\ b & -a & x \end{vmatrix}$.

Expanding the determinant gives x^3 + abc - abc = x^3. Setting this equal to zero results in the equation x^3 = 0. The only value that satisfies this equation is x = 0. Thus, there is exactly 1 real root.

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