jee-main 2024 Q61

jee-main · India · session1_30jan_shift2 Roots of polynomials Existence or counting of roots with specified properties
If $z$ is a complex number, then the number of common roots of the equation $z^{1985} + z^{100} + 1 = 0$ and $z^3 + 2z^2 + 2z + 1 = 0$, is equal to:
(1) 1
(2) 2
(3) 0
(4) 3
If $z$ is a complex number, then the number of common roots of the equation $z^{1985} + z^{100} + 1 = 0$ and $z^3 + 2z^2 + 2z + 1 = 0$, is equal to:\\
(1) 1\\
(2) 2\\
(3) 0\\
(4) 3