If the roots of the equation x^{2}-4x-\log_{10}N=0 are real, then what is the <strong>MINIMUM</strong> value of N?

Explanation

For real roots, D \geq 0 \implies (-4)^2 - 4(1)(-\log_{10}N) \geq 0. This simplifies to 16 + 4\log_{10}N \geq 0 \implies \log_{10}N \geq -4. Thus, N \geq 10^{-4}, so the minimum value is 0.0001.

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