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Question

Let z1 and z2 be roots of the equation z2+pz+q = 0,p,qc,Let A and B represents z1 and z2 in the complex plane. If AoB = α 0, AND OA = OB;O is the origin, then p24q



Your Answer
A

Your Answer
B

Correct Answer
C

Your Answer
D

None of these


Solution

The correct option is C


z2+pz+q = 0

z1+z2 = -p,z1z2= q

OA = OB |z1|=|z2|

z2z1 = eiα = cos α+isin α

z1+z2z1 = 1+cos α+isin α

= 2cosα2(cosα2+isinα2)

= (z1+z2)2z21 = 4cos2α2eiα = 4cos2α2z2z1

= (z1+z2)2 = 4cos2α2z1z2

p2 = 4qcos2α2

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