Jee Main 2024 30 01 2024 Shift 2 - Question6
Question 6
$z^{1985}+z^{100}+1=0$ and
$z^{3}+2 z^{2}+2 z+1=0$
the number of common roots of the equation is
1
2
3
4
Show Answer
Answer: (2)
Solution:
The roots of equation $z^{1985}+z^{100}+1=0$ are $\omega$ and $\omega^{2}$ and also satisfy $z^{3}+2 z^{2}+2 z+1=0$
$\therefore \omega \text{ and } \omega^{2}$ are common solutions.
( $\omega$ is cube root of unity)
$\therefore \text{2}$ solutions
BETA
