Question

If $\alpha ,\beta$ are roots of the equation $x^2-p(x+1)-c=0$, then

$(\alpha +1)(\beta +1)$=

• A. c
• B. c-1
• C. 1-c
• D. none of these

Answer 1

The correct option is C

1-c

Given equation:

$x^2-p(x+1)-c=0$

or

$x^2-px-p-c=0$

Also, $\alpha$ and $\beta$ are the roots of the equation

Sum of the roots $\alpha +\beta$=p.

Product of the roots = $\alpha \beta$=-(c+p)

Then, $\alpha +1$ $\beta +1$= $\alpha \beta$+ $\alpha$ + $\beta$+1 =-(c+p)+p+1

=-c-p+p+1=1-c