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Grade: 11
        

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.

7 years ago

Answers : (2)

vikas askiitian expert
509 Points
							

alfa = p    &   beta = q

aSn+1 +bSn + cSn-1 = 0

taking LHS

= a(pn+1 + qn+1)+b(pn+qn)+c(pn-1+ qn-1)

=[apn+1+bpn+cpn-1] + [aqn+1+bqn+cqn-1]

=pn-1[ap2+bp+c]  + qn-1[aq2+bq+c]

now since p,q are the roots of eq ax2+bx+c=0 so  p,q  will satisfy this eq &

ap2+bp+c = 0 = aq2+bq+c

so the LHS becomes

LHS = 0+0 =0 =RHS

hence proved

7 years ago
jagdish singh singh
173 Points
							

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7 years ago
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