Multiple choice

If the roots of the equation $\displaystyle \frac {\alpha}{x-\alpha}+\displaystyle \frac {\beta}{x-\beta}=1$ be equal in magnitude but opposite in sign, then $\alpha+\beta$ is equal to:

  1. 0

  2. 1

  3. 2

  4. 3
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A Correct answer
Explanation

Let the roots be r and -r. The sum of roots is r + (-r) = 0. For the equation, rearrange to a quadratic form. The sum of roots is -b/a. Solving the equation leads to the condition alpha + beta = 0.

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