For what value of k, the equation x 2 + 2(k - 4) x + 2k = 0 has equal roots?

Given equation is
x² + 2(k - 4)x + 2k = 0
On comparing with ax² + bx + c = 0
Here, a = 1, b = 2(k -4), c = 2k
Since, the root are equal, we have D = 0.
b² - 4ac = 0
∴ 4(k - 4)² - 8k = 0
4(k² + 16 - 8k) - 8k = 0
⇒ 4k² + 64 - 32k - 8k = 0
⇒ 4k² - 40k + 64 = 0
⇒ k² - 10k + 16 = 0
⇒ k² - 8k - 2k + 16 = 0
⇒ k(k - 8) -2 (k - 8) = 0
⇒ (k - 8) (k - 2) = 0
Hence, the value of k 8 or 2.