Question

Find the values of $k$ for which the given quadratic equation has real and distinct roots
$\left(i\right)k{x}^2+2x+1=0$

Answer 1

General quadratic equation is $a{x}^2+bx+c=0$

As per the question, the given equation has real and distinct root.

So, $D>0$

Therefore $D=b^2-4ac=(2{)}^2-4\times k\times 1$

$D=4-4k=4(1-k)$

Therefore $D>0$

$4(1-k)>0=(1-k)>0$

Hence $k<1$