Question

. If α and β are the zeroes of the polynomial f(x) = x2 - p(x + 1) – C, then (α + 1)(β+ 1) is
1 to
a) c-1
(6) 1-c
(d) 1+c
(c) c​

Answer 1

Given :

x² - p(x+1)-c = x² -px-p -c

compare it with ax²+bx+c =0

a= 1, b= -p , c= -p-c

α and β are two zeroes

i) sum of the zeros= -b/a

α+β = - (-p)/1= p -----(1)

ii) product of the zeroes = c/a

αβ = (-p-c) /1 = -p-c -----(2)

now take 

LHS = (α+1)(β+1)

= α(β+1) +1(β+1)

= αβ +α +β +1

= -p-c+p+1  [from (2) and (1) ]

= -c+1

= 1 -c

= RHS