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Let alpha,beta be the roots of the equat...

Let `alpha,beta` be the roots of the equation `ax^2+bx+c=0 "Let" S_n=alpha^n+beta^n "for" n ge 1` evaluate the determinant
`|{:(3,1+s_1,1+s_2),(1+s_1,1+s_2,1+s_3),(1+s_2,1+s_3,1+s_3):}|`

Text Solution

Verified by Experts

The correct Answer is:
`((a+b+c)^2)/(a^4)( b^2-4ac)`
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Let alpha,beta , be the roots of the equation x^2+x-1=0 . Let S_n=alpha^n+beta^n "for" n ge 1 . Evaluate the determinant |{:(3,1+s_1,1+s_2),(1+s_1,1+s_2,1+s_3),(1+s_2,1+s_3,1+s_4):}|

Let alpha , beta be the roots of the equation ax^2 +bx+c=0 . Let S_(n) = alpha^(n)+beta^(n) for ngt1 .Let Delta=|(3,1+s_1,1+s_2),(1+s_1,1+s_2,1+s_3),(1+s_2,1+s_3,1+s_4)| Then Delta =……

Knowledge Check

  • If alpha and beta are the roots of the equation ax^2+bx+c=0 and S_n=alpha^n+beta^n , then a S_(n+1)+b S_n+c S_(n-1) is equal to

    A
    0
    B
    abc
    C
    a+b+c
    D
    None of these

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