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$a,b\in R$,roots of $x^2+ax+b=0$ are $\alpha,\beta$ and roots of $x^2+bx+a=0$ are $\alpha+k,\beta+k$ where $k\neq 0$.If $ab=\lambda$,then interval for $\lambda$ is

$\begin{array}{1 1}(A)\;(-\infty,4)&(B)\;(-\infty,4)\\(C)\;(4,\infty)&(D)\;(4,\infty)\end{array} $

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$ab=\lambda$
$\Rightarrow a+\large\frac{\lambda}{a}$$+4=0$
$\Rightarrow a^2+4a+\lambda=0$
$D >0$
$\Rightarrow 16-4\lambda > 0$
$\Rightarrow \lambda < 4$
$\Rightarrow \lambda \in (-\infty,4)$
Hence (B) is the correct answer.
answered Apr 15, 2014 by sreemathi.v
 

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