Answer 1

Since `alpha` and `beta` are the zeros of quadratic polynomial

f(x) = x² − p(x + 1) − c

`f(x)= x^2 - px -p-c`

`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`

`= -(-p/1)`

`= p`

`alphabeta= (\text{Coefficient of x})/(\text{Coefficient of}x^2)`

`= (-p-c)/1`

`= -p-c`

We have 

`0 = (alpha + 1)(beta+1)`

`0=alpha beta + (alpha +beta)+1`

`0 = - cancel(p)-c + cancel(p) +1`

`0 = -c +1`

The value of c is 1.

Hence, the correct alternative is `(a)`