TS EAMCET · Maths · Determinants
If \(x=k\) satisfies the equation
\(\left|\begin{array}{ccc}x-2 & 3 x-3 & 5 x-5 \\ x-4 & 3 x-9 & 5 x-25 \\ x-8 & 3 x-27 & 5 x-125\end{array}\right|=0\), then \(x=k\) also satisfies the equation
- A \(x^2+x-2=0\)
- B \(x^2-x-6=0\)
- C \(x^2-2 x-8=0\)
- D \(x^2+2 x-3=0\)
Answer & Solution
Correct Answer
(D) \(x^2+2 x-3=0\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { }\left|\begin{array}{ccc}x-2 & 3 x-3 & 5 x-5 \\ x-4 & 3 x-9 & 5 x-25 \\ x-8 & 3 x-27 & 5 x-125\end{array}\right|=0 \\ & \Rightarrow\left|\begin{array}{ccc}x-2 & x-1 & x-1 \\ x-4 & x-3 & x-5 \\ x-8 & x-9 & x-25\end{array}\right|=0 \\ &…
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