given x²-a(x+1)-c=0

x²-ax-a-c=0

x²-ax-(a+c)=0

as α, β are roots of equation, we get

sum of the roots α + β = a

Product of roots αβ = - (a + c)

Given (1+ α) (1+ β)

= 1 + (α + β) + (α β)

= 1 + a – a – c

= 1 – c.