If the equation 2x² - 5x + (k + 3) = 0 has equal roots then the value of k is

1. $\dfrac{9}{8}$

2. $-\dfrac{9}{8}$

3. $\dfrac{1}{8}$

4. $-\dfrac{1}{8}$

Given ,

2x² - 5x + (k + 3) = 0 has equal roots

Comparing equation with ax² + bx + c = 0
a= 2 , b = -5 , c = k + 3

Since, equation has equal roots

∴ b² - 4ac = 0

$\Rightarrow (-5)^2 - 4 \times 2 \times (k + 3) = 0 \\[0.5em] \Rightarrow 25 - 8(k + 3) = 0 \\[0.5em] \Rightarrow 25 - 8k - 24 = 0 \\[0.5em] \Rightarrow 1 - 8k = 0 \\[0.5em] \Rightarrow 8k = 1 \\[0.5em] k = \dfrac{1}{8}$

∴ Option 3 is the correct option.