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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Determinants

NDA 2013 · Mathematics · Determinants

The roots of the equation | array ccc 1 & t-1 & 1 t-1 & 1 & 1 1 & 1...

The roots of the equation \left|1t−11t−11111t−1\begin{array}{ccc}1 & t-1 & 1 \\ t-1 & 1 & 1 \\ 1 & 1 & t-1\end{array}\right|=0$ are

Options

  1. A1,21,2
  2. B−1,2-1,2
  3. C1,−21,-2
  4. D−1,−2-1,-2

Correct answer

B. −1,2-1,2

Step-by-step solution

1(t−2)−(t−1)(t−1)2−1]+1(t−2)=0(t−2)[1−(t−1)(t)+1]=0(t−2)(t2−t−2)=0(t−2)(t−2)(t+1)=0t=2,t=−1\begin{aligned} & \left.1(t-2)-(t-1)(t-1)^2-1\right]+1(t-2)=0 \\ & (t-2)[1-(t-1)(t)+1]=0 \\ & (t-2)\left(t^2-t-2\right)=0 \\ & (t-2)(t-2)(t+1)=0 \\ & t=2, t=-1\end{aligned}
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