Multiple choice

The value of $k$, for which the quadratic equation $4x^{2}+4\sqrt{3}x+k=0$ has equal roots is :

  1. $k = 2$
  2. $k = -2$
  3. $k = -3$
  4. $k = 3$
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D Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant D = b^2 - 4ac must be 0. Here, a=4, b=4*sqrt(3), and c=k. So, (4*sqrt(3))^2 - 4(4)(k) = 0, which simplifies to 48 - 16k = 0, meaning k = 3.

AI explanation

For the equation 4x^2 + 4 times the square root of 3 times x + k = 0 to have equal roots, its discriminant must equal zero, meaning b^2 - 4ac = 0. Substituting the coefficients gives (4 times the square root of 3)^2 - 4(4)(k) = 0, which simplifies to 48 - 16k = 0. Solving for k results in 16k = 48, so k = 3.

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