Common roots of the equations z^3+2z^2+2z+1 = 0 and z^1985 +z^100 +1 = 0 are
Common roots of the equations z3+2z2+2z+1 = 0 and z1985 +z100 +1 = 0 are
(1) ω,ω2
(2) 1, ω,ω2
(3)-1, ω,ω2
(4) -ω, -ω2
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Correct Option (1) ω,ω2
Explanation:
The first equation may be written as
(z+1)(z+z+1) = 0:
its roots are –1,ω and ω2. The root z = -1 does not satisfy the second
equation but z = ω and z = ω2. satisfy it as ω3n = 1 Hence and ω and ω2 are the common roots.
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