If alpha and beta are the roots of the equation ax 2 + bx + c = 0 and S n = (alpha) n + (beta) n , show that aS n+1 + bS n + cS n- 1 = 0 and hence find S 5 .

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vikas askiitian expert · Answer

alfa = p & beta = q aS n+1 +bS n + cS n-1 = 0 taking LHS = a(p n+1 + q n+1 )+b(p n +q n )+c(p n-1 + q n-1 ) =[ap n+1 +bp n +cp n-1 ] + [aq n+1 +bq n +cq n-1 ] =p n-1 [ap 2 +bp+c] + q n-1 [aq 2 +bq+c] now since p,q are the roots of eq ax 2 +bx+c=0 so p,q will satisfy this eq & ap 2 +bp+c = 0 = aq 2 +bq+c so the LHS becomes LHS = 0+0 =0 =RHS hence proved

jagdish singh singh · Answer

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If alpha and beta are the roots of the equation ax 2 + bx + c = 0 and S n = (alpha) n + (beta) n , show that aS n+1 + bS n + cS n- 1 = 0 and hence find S 5 .

If alpha and beta are the roots of the equation ax² + bx + c = 0 and S_n = (alpha)ⁿ + (beta)ⁿ, show that aS_n+1 + bS_n + cS_n-1 = 0 and hence find S₅.

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If alpha and beta are the roots of the equation ax 2 + bx + c = 0 and S n = (alpha) n + (beta) n , show that aS n+1 + bS n + cS n- 1 = 0 and hence find S 5 .

If alpha and beta are the roots of the equation ax2 + bx + c = 0 and Sn = (alpha)n + (beta)n, show that aSn+1 + bSn + cSn-1 = 0 and hence find S5.

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If alpha and beta are the roots of the equation ax² + bx + c = 0 and S_n = (alpha)ⁿ + (beta)ⁿ, show that aS_n+1 + bS_n + cS_n-1 = 0 and hence find S₅.