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If alpha and beta are the roots of x^(2)...

If `alpha` and `beta` are the roots of `x^(2)+x+1=0`, then `alpha^(16)+beta^(16)=`

A

`(-1-isqrt3)/2`

B

1

C

-1

D

`(-1+isqrt3)/2`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • If alpha and beta are the roots of x^(2) - ax + b^(2) = 0, then alpha^(2) + beta^(2) is equal to :

    A
    `a^(2) - 2b^(2)`
    B
    `2a^(2) - b^(2)`
    C
    `a^(2) - b^(2)`
    D
    `a^(2) + b^(2)`

  • If alpha and beta are the roots of x^(2)-ax+b^(2)=0 , then alpha^(2) +beta^(2) is equal to_______

    A
    `2a^(2)-b^(2)`
    B
    `a^(2)+b^(2)`
    C
    `a^(2)-2b^(2)`
    D
    `a^(2)-b^(2)`

  • If alpha, beta are the roots of ax^(2) - 26x + c = 0 , then alpha^(3) beta^(3) + alpha^(2) beta^(3) + alpha^(3) beta^(2) equals :

    A
    `(c^(2))/(a^(3)) (c + 26) `
    B
    `(c^(2))/(a^(3)) (c - 26)`
    C
    `(bc^(3))/(a^(3))`
    D
    None of these

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