Question

if a and b are zeroes of quadratic polonomial f(t) = t2 -p(t-1)-c ,show that (a+1) (b+1) = 1-c

Answer 1

given a,b are zeroes of f(t)
where
f(t)=t2-p(t-1)-c
f(a)=a2-p(a-1)-c
f(b)=b2-p(b-1)-c
(t-a)(t-b)=0
t2-t(a+b)+ab=0.
compared above eqn with f(t)
we get, a+b=-p,a b=p-c
(a+1)(b+1)=ab+(a+b)+1=p-c-p+1=1-c