Find the value (s) of k, if the quadratic equation 3x² – k√3x + 4 = 0 has equal roots.

We have quadratic equation,

3x² - k√3x + 4 = 0

Comparing this equation with standard quadratic equation, ax² + bx + c = 0

We have a = 3, b = -k√3 and c = 4

We have quadratic formula,

(b² – 4ac) is called discriminant (or D).

Now, since the roots of this quadratic equation are same,

D = 0

⇒ b² – 4ac = 0 …(i)

Substituting values a = 3, b = -k√3 and c = 4 in equation (i), we get

(-k√3)² – 4(3)(4) = 0

⇒ 3k² – 48 = 0

⇒ 3k² = 48

⇒ k² = 16

⇒ k = √16

⇒ k = 4

Thus, k has two values, i.e., 4 and -4.