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

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


16