Guest

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.

Grade:11

2 Answers

vikas askiitian expert
509 Points
11 years ago

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

jagdish singh singh
173 Points
11 years ago

274_24699_199.gif

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free