Question

If α, β are the zeros of polynomial f(x) = x² − p (x + 1) − c, then (α + 1) (β + 1) =

Options

• c − 1

• 1 − c

• c

• 1 + c

Answer 1

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

f(x) = x² − p (x + 1) − c

`= x^2 - px p -c`

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

`=-((-p)/1)`

`= p`

`alpha xx ß = (\text{constat term})/(text{coefficient of} x^2)`

`= (-p-c)/1`

`= -p-c`

We have

`(alpha+1)(beta+1)`

`= alpha beta+ beta + alpha +1`

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

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

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

`= -c+1`

`= 1-c`

The value of `(alpha +1) (beta +1)` is ` 1- c`.

Hence, the correct choice is  `(b)`