Q3 of 108 Page 44

Find these values of k for which the roots of the following quadratic equations are real and distinct:

kx2 + 2x + 1 = 0


When we compare the above quadratic equation with the generalized one we get,

ax2 + bx + c = 0


a = k


b = 2


c = 1


Since the quadratic equations have real and distinct roots,


b2 – 4ac > 0 for real and distinct roots


⟹ (2) 2 – (4 × k × 1) > 0


⟹ 4 – 4k > 0


⟹ 4k < 4 [Dividing both sides by 4]


⟹ k < 1


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