The set of all values of $k$ for which the quadratic equation $k{x}^2+2x+1=0$ has real and distinct roots is

Solution

1. For the equation to be quadratic, $k\ne 0$.
2. For real and distinct roots, the discriminant $D=b^2-4ac>0$.
3. Here $$\begin{array}{rl}D& =2^2-4(k)(1)\\ & =4-4k\end{array}$$.
4. Setting $4 - 4k > 0$ gives $k<1$.
5. Combining $k<1$ and $k\ne 0$, we get the result.
6. Hence the answer is (C).