Let $a,$ $b,$ $c$ be nonzero real numbers.  Find the number of real roots of the equation
\[\begin{vmatrix} x & c & -b \\ -c & x & a \\ b & -a & x \end{vmatrix} = 0.\]
Question:
Let $a,$ $b,$ $c$ be nonzero real numbers.  Find the number of real roots of the equation
\[\begin{vmatrix} x & c & -b \\ -c & x & a \\ b & -a & x \end{vmatrix} = 0.\]
Answer:
Let's think step by step.

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1
Let $a,$ $b,$ $c$ be nonzero real numbers.  Find the number of real roots of the equation
\[\begin{vmatrix} x & c & -b \\ -c & x & a \\ b & -a & x \end{vmatrix} = 0.\]
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