Q7 of 168 Page 7

Find the value of k, so that the quadratic equation

(k + 1) x2 – 2 (k — 1) x + 1 = 0 has equal roots.

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 = 3k


k2 – 3k = 0


k(k – 3) = 0


k = 0 or k – 3 = 0


k = 3


∴ Values of k are 0, 3.


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