What is the condition on real coefficients a, b for x^2 + ax + b to have two distinct purely imaginary roots?

Answer and explanation

Correct answer: C. a = 0 and b > 0

  1. Step 1: Roots are (-a +/- sqrt(a^2 - 4b)) / 2. For roots to be purely imaginary, real part must be 0 => a = 0. Step 2. When a = 0, roots are +/- sqrt(-4b)/2 = +/- sqrt(-b). For these to be non-zero imaginary, -b < 0 => b > 0. Answer: a = 0 and b > 0. Why not the others: If b < 0, x^2 - |b| = 0 gives real roots +/- sqrt(|b|).

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