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If \((2+i)\) is a root of the equation \(x^3-5 x^2+9 x-5=0\), then the other roots are
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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.
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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