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If alpha, beta are the roots of the equ...

If ` alpha, beta` are the roots of the equation ` x^(2) - 2x + 4 = 0 ` then for any ` n in N` show that ` alpha^(n) + beta^(n) = 2^(n+1) cos ((n pi)/3)`.

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Knowledge Check

  • If alpha and beta are the roots of the equation x^2-2x+4=0, then alpha ^9 + beta ^9=

    A
    `-2^8`
    B
    ` 2^9`
    C
    `-2^10`
    D
    `2^10`

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    A
    `2^(12)`
    B
    `2^(10)`
    C
    `2^(13)`
    D
    `-2^(13)`

  • If alpha, beta are the roots of the equation x^(2)+7x+12=0 , then the equation whose roots are (alpha+beta)^(2) and (alpha-beta)^(2) is

    A
    `x^(2)+50x+49=0`
    B
    `x^(2)-50x+49=0`
    C
    `x^(2)-50x-49=0`
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