Question

If alpha and beta are the zeros of the quadratic polynomial the f(x) =x²-p(x+1)-c,show that (alpha +1)(beta +1) =1-c

Answer 1

f(x) =x²-p(x+1)-c
=X2  -px – p – c

Then given X2  -px – p – c has zero α and β

α+β= -(-p/1) = p

αβ= (-p*-c)/1= (-p*-c)

we have to prove that, 

(alpha +1)(beta +1) =1-c

LHS

=( α+1)(β+1)

=αβ + α+β +1

= -p-c +p+1

=1-c

=RHS