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If z is a complex number, then the number of common roots of the equations z1985+z100+1=0 and z3+2z2+2z+1=0, is equal to
(2) 2
z3+2z2+2z+1=(z+1)(z2-z+1)+2z(z+1)=(z+1)(z2+z+1)
roots: -1, , 2, where 3=1 and 1+ + 2=0
z=-1: (-1)1985+(-1)100+1=1 0 not common
z= : 1985+ 100+1= 2+ +1=0 common
z= 2: 3970+ 200+1= + 2+1=0 common
∴ number of common roots =2
Answer: (2)
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