Let z be a complex number satisfying z2+2zλ+1=0, where λ is a parameter which can take any real value.
One root lies inside the unit circle and one outside if
A
−1<λ<1
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B
λ>1
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C
λ<1
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D
None of these
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Solution
The correct option is Bλ>1 z=−λ±√λ2−1 λ>1⇒λ2−1>0 z=−λ±√λ2−1,0),(−λ−√λ2−1,0). One root lies inside the unit circle and the other root lies outside the unit circle.