Question

If $1-p$ is a root of the equation $x^2+px+1-p=0$, then the roots of the equation are

• A. $-1,0$
• B. $-1,1$
• C. $-2,1$
• D. $0,1$

Answer 1

The correct option is A $-1,0$

Let $\alpha$ be the other root.
Then, sum of roots $=\alpha +1-p=-p$
$\Rightarrow \alpha =-1$
Product of roots $=\alpha (1-p)=1-p$
$\Rightarrow p-1=1-p$
$\Rightarrow p=1$
Roots are $\alpha ,1-p$
i.e., roots are $-1,0$