Find the values of $k$ for which the equations $k x^{2} + 2 x + 1 = 0$ has real and distinct roots.

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Solution

$k x^{2} + 2 x + 1 = 0$

$b^{2} - 4 a c > 0$

$2^{2} - 4 (k) (1) > 0$

$4 (1 - k) > 0$

$(k - 1) < 0$

$k < 1$

$k (- \infty, 1)$

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