Find the value of k for which the quadratic equation kx^2 + 2x + 1 = 0 has a real and distinct root.

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Solution

$The given quadratic equation is, {kx}^{2} + 2 x + 1 = 0 Now, a = k; b = 2; c = 1 Now, D = b^{2} - 4 ac = {(2)}^{2} - 4 (k) (1) = 4 - 4 k For real and distinct roots, D > 0 \Rightarrow 4 - 4 k > 0 \Rightarrow 4 > 4 k \Rightarrow 4 k < 4 \Rightarrow k < 1$

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