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Question: Answered & Verified by Expert
If \((2+i)\) is a root of the equation \(x^3-5 x^2+9 x-5=0\), then the other roots are
MathematicsComplex NumberAP EAMCETAP EAMCET 2020 (21 Sep Shift 1)
Options:
  • A 1 and \((2-i)\)
  • B -1 and \((3+i)\)
  • C 0 and 1
  • D -1 and \((-2+i)\)
Solution:
2090 Upvotes Verified Answer
The correct answer is: 1 and \((2-i)\)
It is given that \(2+i\) is the root of the equation \(x^3-5 x^2+9 x-5=0\), so another non-real complex root will be \(2-i\).
Now, let the third root is \(\alpha\), so by product of roots, we have
\((2+i)(2-i) \alpha=5 \Rightarrow \alpha=1\)
Hence, option (a) is correct.

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