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(C) Let the roots of the equation $x^4 - 2ax^3 + 4bx^2 + 8ax + 16 = 0$ be $\alpha, \beta, \gamma, \delta$. From the properties of the roots,the produc

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$\frac{1}{2}$

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(C) Let the roots of the equation $x^4 - 2ax^3 + 4bx^2 + 8ax + 16 = 0$ be $\alpha, \beta, \gamma, \delta$. From the properties of the roots,the product of the roots is $\alpha \beta \gamma \delta = \frac{16}{1} = 16$. Let the roots of the new equation be $p\alpha, p\beta, p\gamma, p\delta$. Since the new equation is a reciprocal equation,the product of its roots must be $1$. Thus,$(p\alpha)(p\beta)(p\gamma)(p\delta) = 1$. $p^4(\alpha \beta \gamma \delta) = 1$. Substituting the product of the roots,we get $p^4(16) = 1$. $p^4 = \frac{1}{16}$. $|p|^4 = (\frac{1}{2})^4$. Therefore,$|p| = \frac{1}{2}$.

If the equation whose roots are $p$ times the roots of $x^4 - 2ax^3 + 4bx^2 + 8ax + 16 = 0$ is a reciprocal equation,then $|p| = $

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