Question

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2 - p(x+1)-c, show that (Alfa+ 1) (beta+1) = 1-c

Answer 1

x^2 - p(x+1) - c

=x^2 - px - p - c

=x^2 - px -(p+c)

Here,a_1
b_(-p)
c_ -(p+c)

Alpha+ beta =p
Alpha × beta= -(p+c)

(Alpha+1)(beta+1)

(Alpha×beta) + alpha + beta +1

[Substitute the values]
-p-c+p+1.

i.e,1-c

Hence verified,