JEE Main On 08 April 2018 Question 3
Question: If $ \alpha ,\beta \in C $ are the distinct roots, of the equation $ x^{2}-x+1=0, $ then $ {{\alpha }^{101}}+{{\beta }^{107}} $ is equal to: [JEE Main Online 08-04-2018]
Options:
A) 1
B) 2
C) -1
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
- 1 Roots of $ x^{2}-x+1=0 $ are $ (-\omega ,-{{\omega }^{2}}) $
$ \Rightarrow \alpha =-\omega ,\beta =-{{\omega }^{2}} $
$ \Rightarrow {{\alpha }^{101}}+{{\beta }^{107}} $
$ \Rightarrow {{(-\omega )}^{101}}+{{(-{{\omega }^{2}})}^{107}} $
$ \Rightarrow -{{\omega }^{2}}-\omega =1 $
