Question

If α, β are the two zeroes of the polynomial f(x) = x² – p (x +1) – c, then (α + 1)(β + 1) = ……………

A) c – 1 

B) 1 – c 

C) c 

D) 1 + c

Answer 1

Correct option is (B) 1 – c

f(x) = \(x^2-p(x+1)-c\)

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

\(\therefore\) \(\alpha+\beta\) \(=\frac{-(-p)}1\) = p

\(\alpha\beta\) \(=\frac{-(p+c)}1\) = -(p+c)

Now, \((\alpha+1)(\beta+1)\) \(=\alpha\beta+\alpha+\beta+1\)

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

= 1 - c

Answer 2

Correct option is B) 1 – c