Find the value(s) of k, if the quadratic equation 3x 2 − k√3 x + 4 = 0 has equal roots.

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Question 2 Find the value(s) of k, if the quadratic equation 3x2 − k√3 x + 4 = 0 has equal roots. 3x2 – k√3 x + 4 = 0 Comparing equation with ax2 + bx + c = 0 a = 3, b = – k√3 , c = 4 Since the equation has 2 equal roots, D = 0 b2 – 4ac = 0 Putting values ("– k" √3)^2 – 4×3×4=0 3k2 – 48 = 0 3k2 = 48 k2 = 48/3 k2 = 16 k = ±√16 k = ± √(4 ×4) k = ± 4 ∴ k = ± 4

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