TS EAMCET · Maths · Determinants
The sum of all the roots of the equation \(\left|\begin{array}{ccc}x & -3 & 2 \\ -1 & -2 & (x-1) \\ 1 & (x-2) & 3\end{array}\right|=0\) is
- A \(13\)
- B \(3\)
- C \(2\)
- D \(7\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\( x[(-2)(3) - (x-1)(x-2)] - (-3)[(-1)(3) - (x-1)(1)] + 2[(-1)(x-2) - (-2)(1)] = 0 \) \( x[-6 - (x^2 - 3x + 2)] + 3[-3 - x + 1] + 2[-x + 2 + 2] = 0 \) \( x[-x^2 + 3x - 8] + 3[-x - 2] + 2[-x + 4] = 0 \) \( -x^3 + 3x^2 - 8x - 3x - 6 - 2x + 8 = 0 \) \( -x^3 + 3x^2 - 13x + 2 = 0 \)…
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