If the equation 3x² - kx + 2k = 0 has equal roots, then the value(s) of k is (are)

1. 6
2. 0 only
3. 24 only
4. 0 or 24

Given ,

3x² - kx + 2k = 0 has equal roots

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

Since, equation has equal roots

∴ b² - 4ac = 0

$\Rightarrow (-k)^2 - 4 \times 3 \times 2k = 0 \\[0.5em] \Rightarrow k^2 - 24k = 0 \\[0.5em] \Rightarrow k(k - 24) = 0 \\[0.5em] \Rightarrow k = 0 \text{ or } k - 24 = 0 \\[0.5em] k = 0 \text{ or } k = 24 \\[0.5em]$

∴ Option 4 is the correct option.