Multiple choice

If the roots of the equation x2 - 4x - log10N = 0 are real, then what is the minimum value of N?

  1. 0.1

  2. 0.01

  3. 0.001

  4. 0.0001
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For real roots, the discriminant D >= 0. D = (-4)^2 - 4(1)(-log10 N) = 16 + 4 log10 N. 16 + 4 log10 N >= 0 => 4 log10 N >= -16 => log10 N >= -4. N >= 10^-4 = 0.0001.

AI explanation

For the roots to be real, the discriminant must be greater than or equal to zero, meaning 16 plus 4 times log10N must be greater than or equal to zero. Solving this inequality gives log10N greater than or equal to -4. Therefore, the minimum value of N is 10 to the power of -4, which is 0.0001.

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