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

We know that the quadratic equation has equal roots, when the discriminant, D = 0.

Given quadratic equation is x² + 2(k – 4) x + 2k = 0

Here, a = 1, b = 2k – 8 and c = 2k.

As D = 0, b² – 4ac = 0

Now, substitute the values, we get

(2k – 8)² – 4(1)(2k) = 0

4k² – 32k +64 – 8k = 0

4k² – 40k + 64 = 0

4(k² – 10k + 16) = 0

K² – 10k + 16 = 0

Now, factorise the above equation, we get

K² – 8k – 2k + 16 = 0

k (k-8) -2 (k-8) = 0

⇒ (k-2) = 0 and (k -8) = 0

⇒ k = 2 and k = 8

Hence, the value of k = 2 or 8