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If alpha,beta are the roots of x^2+p x+q...

If `alpha,beta` are the roots of `x^2+p x+q=0a d nx^(2n)+p^n x^n+q^n=0a n di lf(alpha//beta),(beta//alpha)` are the roots of `x^n+1+(x+1)^n=0,t h e nn( in N)` a. must be an odd integer b. may be any integer c. must be an even integer d. cannot say anything

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`alpha + beta = - p, alpha beta = q`
and `alpha^(2n) + p^(n)alpha^(n) + q^(n) = 0`
`beta^(2n) + p^(n)beta^(n) + q^(n) = 0`
`alpha^(n) + beta^(n) = -p^(n)`
`alpha^(n)beta^(n) = q^(n)`
`((alpha)/(beta))^(n) + 1 + ((alpha)/(beta) + 1)^(n) = 0`
`alpha^(n) + beta^(n) + (alpha + beta)^(n) = 0`
`alpha^(n) + beta^(n) + (alpha + beta)^(n) = 0`
`-p^(n) + (-p)^(n) = 0`
possible only when `n = even`
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