Find the Value(s) of k for which the quadratic equation 2x² – kx + k = 0 has equal roots.

Given: quadratic equation 2x² – kx + k = 0 has equal roots.

To find: The value of k.

Formula Used:

If a quadratic equation

ax² + bx + c = 0, a ≠ 0 has two equal roots, then its discriminant value will be equal to zero i.e.,

D = b² - 4ac = 0

Explanation:

Given, 2x² – kx + k = 0

For equal roots,

D = b² - 4ac = 0

⇒ (-k)² - 4(2)(k) = 0

⇒ k² - 8k = 0

⇒ k (k - 8) = 0

⸫ k = 0,8