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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2016 · Mathematics · Quadratic Equation

If both the roots of the equation x^2-2 k x+k^2-4=0 lie between -3...

If both the roots of the equation x2−2kx+k2−4=0x^2-2 k x+k^2-4=0 lie between -3 and 5 , then which one of the following is correct?

Options

  1. A−2<k<2-2 < \mathrm{k} < 2
  2. B−5<k<3-5 < \mathrm{k} < 3
  3. C−3<k<5-3 < k < 5
  4. D−1<k<3-1 < \mathrm{k} < 3

Correct answer

D. −1<k<3-1 < \mathrm{k} < 3

Step-by-step solution

x2−2kx+k2−4=0\mathrm{x}^2-2 \mathrm{kx}+\mathrm{k}^2-4=0⇒(x−k)2−22=0⇒(x−k−2)(x−k+2)=0⇒x=k+2,k−2⇒k+2<5k−2>−3⇒k<3k>−1⇒−1<k<3\begin{array}{ll}\Rightarrow & (\mathrm{x}-\mathrm{k})^2-2^2=0 \\ \Rightarrow & (\mathrm{x}-\mathrm{k}-2)(\mathrm{x}-\mathrm{k}+2)=0 \\ \Rightarrow & \mathrm{x}=\mathrm{k}+2, \mathrm{k}-2 \\ \Rightarrow & \mathrm{k}+2 < 5 & \mathrm{k}-2 > -3 \\ \Rightarrow & \mathrm{k} < 3 & \mathrm{k} > -1 \\ \Rightarrow & -1 < \mathrm{k} < 3\end{array}$$
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