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If alpha and beta be the roots of the eq...

If `alpha` and `beta` be the roots of the equation `x^(2)-2x+2=0`, then the least value of `n` for which `((alpha)/(beta))^(n)=1` is:

A

5

B

3

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`x^2-2x+2=0 alpha & beta` are roots
`alpha=(2+sqrt-4)/2=1+i," " beta=(2-sqrt-4)/2=1-i`
`alpha/beta=(1+i)/(1-i)=i`
`(alpha/beta)^n=(i)=1`
Least value of n =4
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