find the value of k so they have equal roots. (k_1)x² _ 2(k_1)x_1 = 0
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well
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Since roots are equal ∴ d=0 ….(1) (k + 1)x2 - 2 (k – 1) x + 1 = 0 d = b2 – 4ac d = (–2(k–1))2– 4(k+1)(1) d = (–2k+2)2 – 4k – 4 d = 4k2 + 4 – 8k – 4k – 4 (∵ (a + b)2 = a2 + b2 + 2ab) d = 4k2 – 12k From (1), d = 0 ∴ Equation will be: 0 = 4k2 – 12k 4k2 = 12k k2 = 12/4 k k2 = 3k k2 – 3k = 0 k(k – 3) = 0 k = 0 or k – 3 = 0 k = 3 ∴ Values of k are 0, 3.Read more on Sarthaks.com - https://www.sarthaks.com/939417/find-the-value-of-k-so-that-the-quadratic-equation-k-1-x-2-2-k-1-x-1-0-has-equal-roots
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