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If both the roots of the equation $x^{2}-2 k x+k^{2}-4=0$ lie between $-3$ and 5 , then which one of the following is correct?
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The correct answer is:
$-1 < \mathrm{k} < 3$
$\begin{aligned} & x^{2}-2 k x+k^{2}-4=0 \\ & \Rightarrow(x-k)^{2}-2^{2}=0 \\ & \Rightarrow(x-k-2)(x-k+2)=0 \\ & \Rightarrow x=k+2, k-2 \\ & \Rightarrow k+2 < 5 \& k-2>-3 \\ & \Rightarrow k < 3 \& k>-1 \\ & \Rightarrow-1 < k < 3 \end{aligned}$
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