If the equation (k + 1)x² - 2(k - 1)x + 1 = 0 has equal roots, then the values of k are

1. 1, 3

2. 0, 3

3. 0, 1

4. 0, $\dfrac{3}{4}$

Given ,

(k + 1)x² - 2(k - 1)x + 1 = 0 has equal roots

Comparing equation with ax² + bx + c = 0
a= (k + 1) , b = -2(k - 1) , c = 1

Since, equation has equal roots

∴ b² - 4ac = 0

$\Rightarrow (-2(k - 1))^2 - 4 \times (k + 1) \times 1 = 0 \\[0.5em] \Rightarrow 4(k^2 + 1 - 2k) - 4(k + 1) = 0 \\[0.5em] \Rightarrow 4k^2 + 4 - 8k - 4k - 4 = 0 \\[0.5em] \Rightarrow 4k^2 - 12k = 0 \\[0.5em] \Rightarrow 4k(k - 3) = 0 \\[0.5em] \Rightarrow 4k = 0 \text{ or } k - 3 = 0 \\[0.5em] k = 0 \text{ or } k = 3.$

∴ Option 2 is the correct option.