If the sum of the roots of the equation x^2-k^2x+30kx-161x-64=0 is zero, then what is the difference of the roots?

Explanation

The sum of the roots is the coefficient of x inverted: k^2 - 30k + 161 = 0. Regardless of k, if the sum of the roots is 0, the equation simplifies to x^2 - 64 = 0 \implies x = \pm 8. The difference of the roots is 8 - (-8) = 16.

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