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

A) 0
B) 1
C) 2
D) none of these

Correct Answer:

A) 0

Description for Correct answer:
Given equation \( \Large \frac{ \alpha }{x- \alpha }+\frac{ \beta }{x- \beta }=1 \) can be rewritten as \( \Large x^{2}-2 \left( \alpha + \beta \right)x+3 \alpha \beta =0 \)

Let roots be \( \Large \alpha' and\ - \alpha' \)

=> \( \Large \alpha' + \left(- \alpha' \right)=2 \left( \alpha + \beta \right) \)

=> \( \Large 0=2 \left( \alpha + \beta \right) \)

=> \( \Large \alpha + \beta = 0 \)

Part of solved Quadratic Equations questions and answers : >> Elementary Mathematics >> Quadratic Equations

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Similar Questions

1). If the roots of the equation \( \Large px^{2}+2qx+r=0 \) and \( \Large qx^{2}-2\sqrt{pr}x+q=0 \) be real, then:

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