Question

$(k+1)x^2-2(k-1)x+1=0$

• A. $0or3$
• B. $1or3$
• C. $0or2$
• D. None of these

Answer 1

The correct option is A $0or3$

$\Rightarrow$ Given quadratic equation is $(k+1)x^2-2(k-1)+1=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $a=(k+1),b=-2(k-1)$ and $c=1$

$\Rightarrow$ It is given that roots are real and equal.

$\therefore$ $b^2-4ac=0$

$\Rightarrow$ $(-2(k-1){)}^2-4(k+1\left)\right(1)=0$

$\Rightarrow$ $4(k-1{)}^2-4k-4=0$

$\Rightarrow$ $4(k^2-2k+1)-4k-4=0$

$\Rightarrow$ $4(k^2-2k+1-k-1)=0$

$\Rightarrow$ $k^2-3k=0$

$\Rightarrow$ $k(k-3)=0$

$\Rightarrow$ $k=0$ and $k-3=0$

$\therefore$ $k=0$ or $k=3$