If `alphaa n dbeta` are the roots of `ax^2+bx+c=0a n dS_n=alpha^n+beta^n,` then `a S_(n+1)+b S_n+c S_(n-1)=0` and hence find `S_5dot`

If alpha , beta are the roots of the equation ax^(2)+bx+c=0 and S_(n)=alpha^(n)+beta^(n) , then aS_(n+1)+bS_(n)+cS_(n-1)=(n ge 2)

If alpha and beta are the rootsof he equations x^2-a x+b=0a n dA_n=alpha^n+beta^n , then which of the following is true? a) A_(n+1)=a A_n+b A_(n-1) b) A_(n+1)=b A_(n-1)+a A_n c) A_(n+1)=a A_n-b A_(n-1) d) A_(n+1)=b A_(n-1)-a A_n

Let alpha,beta be the roots of x^2-x-1=0 and S_n=alpha^n+beta^n , for all integers nge1 . Then for every integer nge2 ,

Let alphaandbeta be the roots of x^(2)+x+1=0 . If n be positive integer, then alpha^(n)+beta^(n) is

Let alpha, beta be the roots of x^(2)-x-1=0 and S_(n)=a^(n)+beta^(n) , for all integers n ge 1 . Then for every integer n gt 2 ,

If alpha,beta are the roots of x^2+px+q =0 and also of x^(2n)+p^n x^n+q^n=0 and if alpha/beta,beta/alpha are root of x^n+1+(x+1)^n =0, then n is

If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n di f(alpha//beta),(beta//alpha) are the roots of x^n+1+(x+1)^n=0,t h e nn( in N) a. must be an odd integer b. may be any integer c. must be an even integer d. cannot say anything

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a. a b c b. a+2b+c c. -1 d. 0

Let alpha ,beta denote the cube roots of unity other than 1 and alpha ne beta let S=underset(n=0)overset302sum(-1)^n(alpha/beta)^n then the value of S is

If S_(n) be the sum of n consecutive terms of an A.P. show that, S_(n+3) - 3S_(n+2) + 3S_(n+1) - S_(n) = 0