Question

Let $z$ be a complex number satisfying $z^2+2z\lambda +1=0$, where $\lambda$ is a parameter which can take any real value, then the roots of this equation lie on a certain circle if,

• A. $-1<\lambda <1$
• B. $\lambda >1$
• C. $\lambda <1$
• D. None of these

Answer 1

The correct option is A $-1<\lambda <1$

For the roots to lie on certain circle in complex plane.
$b^2-4ac<0$

$\therefore 4{\lambda }^2-4<0$

$\therefore {\lambda }^2<1$

$\therefore \lambda <|1|$

$-1<\lambda <1$

Hence option ${}^{\prime }{A}^{\prime }$ is the answer.