If `alpha, beta` be the real roots of `ax^2+bx+c=0`, and `s_n=alpha^n + beta^n` then prove that `as_n + bs_(n-1)+cs_(n-2)=0`.for all `n in N`. Hence or otherwise prove that `|(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)|>=0` for all real `a,b,c.

If alpha&beta be the real roots of ax^(2)+bx+c=0 and s_(n)=alpha^(n)+beta^(n) then prove that as_(n)+bs_(n-1)+cs_(n-2)=0 for all that n ge 2, n in N . Hence or otherwise prove that |{:(,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)):}|ge 0 for all real a,b,c

alpha and beta are the roots of x^2-x-1=0 and S_n=2023 alpha^n 2024 beta^n then

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

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 , 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 , 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 , 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 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