Complex Numbers And Quadratic Equations question 268
Question: The common roots of the equations $ x^{12}-1=0 $ , $ x^{4}+x^{2}+1=0 $ are [EAMCET 1989]
Options:
A) $ \pm \omega $
B) $ \pm {{\omega }^{2}} $
C) $ \pm \omega ,\pm {{\omega }^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ x^{12}-1=(x^{6}+1)(x^{6}-1)=(x^{6}+1)(x^{2}-1)(x^{4}+x^{2}+1) $ Common roots are given by $ x^{4}+x^{2}+1=0 $
$ \therefore $ $ x^{2}=\frac{-1\pm i\sqrt{3}}{2}=\omega ,{{\omega }^{2}} $ or $ {{\omega }^{4}},{{\omega }^{2}} $ $ (\because {{\omega }^{3}}=1) $ or $ x=\pm {{\omega }^{2}},\pm \omega $
BETA
