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

Explanation

For real roots, discriminant D \geq 0. Thus, (-4)^2 - 4(1)(-\log_{10}N) \geq 0 \Rightarrow 16 + 4\log_{10}N \geq 0. This gives \log_{10}N \geq -4, meaning N \geq 10^{-4} = \frac{1}{10000}.

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