JEE Advanced Model Paper 5 with solutions for online practice

Answer (A, B)
z2 + 2λz + 1 = 0
∴ z = -λ ± √λ2−1
∴ z = -λ ± i √1−λ2 if - 1 < λ < 1
or z = -λ ± Ki , where √1−λ2 = K > 0
∴ z + λ = Ki or

––––––

z+λ

= - Ki
∴ (z + λ) (

––––––

z+λ

) = K2
|z + λ| = K
∴ z lies on a circle with centre –λ and radius K
If λ > 1 , we have
z = -λ + √1−λ2 or -λ - √1−λ2
∴ z = - λ + K1 or z = -λ - K1
where K12 = λ2 - 1
⇒ z = - λ ± K1
if z1 and z2 are roots then |z1| = |−λ+K1|
and |z2| = |λ + K1|
|z1||z2| = |K12−λ2| = 1
⇒ |z1| < 1 then |z2| > 1
∴ If one root inside circle then other is outside.