Find the Values of k for Which the Equation Has Real and Distinct Roots
Solution
Given: $$kx^2+2x+1=0$$
Here, $$a=k,\quad b=2,\quad c=1$$
For real and distinct roots, $$D=b^2-4ac>0$$
$$2^2-4(k)(1)>0$$
$$4-4k>0$$
$$1-k>0$$
$$k<1$$
Since the equation is quadratic, $$k\neq0$$
Answer
The quadratic equation has real and distinct roots for $$\boxed{k<1,\; k\neq0}$$