Q17 of 82 Page 4

Find the values of k for which the quadratic equation has equal roots. Also, find these roots. (CBSE 2014)

For a quadratic equation, ax2 + bx + c = 0,


D = b2 – 4ac


If D = 0, roots are equal



⇒ D = 4(k + 1)2 – 4(3k + 1) = 0


⇒ k2 + 2k + 1 – 3k – 1 = 0


⇒ k(k – 1) = 0


⇒ k = 0, 1


When k = 0,


Eq. – x2 + 2x + 1 = 0


⇒ (x + 1)2 = 0


⇒ x = -1


When k = 1,


Eq. – 4x2 + 4x + 1 = 0


⇒ (2x + 1)2 = 0


⇒ x = -1/2

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