Multiple choice

What is the number of real roots of the equation A2/x + B2/(x - 1) = 1, where A and B are real numbers not equal to zero?

  1. 0

  2. 1

  3. 1 or 2

  4. 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Multiplying the equation by x(x - 1) yields the quadratic equation x^2 - (A^2 + B^2 + 1)x + A^2 = 0. The discriminant of this quadratic is ((A - 1)^2 + B^2)((A + 1)^2 + B^2), which is strictly positive because B is non-zero. Thus, the equation always has exactly two distinct real roots, neither of which can be 0 or 1.

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