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Question: Answered & Verified by Expert
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?
MathematicsQuadratic EquationNDANDA 2016 (Phase 2)
Options:
  • A $-2 < \mathrm{k} < 2$
  • B $-5 < \mathrm{k} < 3$
  • C $-3 < \mathrm{k} < 5$
  • D $-1 < \mathrm{k} < 3$
Solution:
2140 Upvotes Verified Answer
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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