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
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