If the roots of the equation (α)/(x-α)+(β)/(x-β)=1 be equal in magnitude but opposite in sign, then α+β is equal to

Correct answer: (A) 0. Given equation can be rewritten as x^2-2(α+β) x+3 α β=0 Let roots be α^′ and -α^′ . ∴ α^′+ (-α^′ )=2(α+β) ⇒ α+β=0

Q98 / 200 · Manipal (MET) 2011 · Mathematics

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

Correct answer
A
0
B
1
C
2
D
None of these

Solution

Given equation can be rewritten as $x^2-2(\alpha+\beta) x+3 \alpha \beta=0$ Let roots be $\alpha^{\prime}$ and $-\alpha^{\prime}$. $\therefore \quad \alpha^{\prime}+\left(-\alpha^{\prime}\right)=2(\alpha+\beta)$ $\Rightarrow \quad \alpha+\beta=0$

Hence, the correct answer is option: 'A'.

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

Solution

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