Complex Numbers And Quadratic Equations question 285
Question: If $ \frac{1+\sqrt{3}i}{2} $ is a root of equation $ x^{4}-x^{3}+x-1=0 $ then its real roots are [EAMCET 2002]
Options:
A) 1, 1
B) - 1, - 1
C) 1, - 1
D) 1, 2
Show Answer
Answer:
Correct Answer: C
Solution:
$ x^{4}-x^{3}+x-1=0 $
Þ $ x^{3}(x-1)+1(x-1)=0 $ $ x-1=0 $ or $ x^{3}+1=0 $
Þ $ x=1,-1,\frac{1+\sqrt{3}i}{2},\frac{1-\sqrt{3}i}{2} $ so its real roots are 1 and - 1.
BETA
