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If alpha&beta be the real roots of ax^(2...

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

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