Answer :

We have quadratic equation,

3x^{2} - k√3x + 4 = 0

Comparing this equation with standard quadratic equation, ax^{2} + bx + c = 0

We have a = 3, b = -k√3 and c = 4

We have **quadratic formula**,

(b^{2} – 4ac) is called discriminant (or D).

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

D = 0

⇒ b^{2} – 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

⇒ 3k^{2} – 48 = 0

⇒ 3k^{2} = 48

⇒ k^{2} = 16

⇒ k = √16

⇒ k = 4

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

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