Let Z1 and Z2 be roots of the equation z + pz + q = 0, where the coefficients p and q may be complex numbers. Let A and B represent z₁ and z2 in the complex plane, respectvely. If ZAOB = 0#0 and OA = OB, where O is the origin, prove that p² = 4q cos² (8/2). 2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let z₁ and z₂ be roots of the equation z + pz + q = 0, where
the coefficients p and q may be complex numbers. Let A and
B represent z₁ and 22 in the complex plane, respectvely. If
ZAOB=0#0 and OA = OB, where O is the origin, prove that
p² = 4q cos² (0/2).
Transcribed Image Text:Let z₁ and z₂ be roots of the equation z + pz + q = 0, where the coefficients p and q may be complex numbers. Let A and B represent z₁ and 22 in the complex plane, respectvely. If ZAOB=0#0 and OA = OB, where O is the origin, prove that p² = 4q cos² (0/2).
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