To determine the value of k in the equation 2x² + kx + 3 = 0, we need to use the discriminant of the quadratic equation.
1. The discriminant (D) of a quadratic equation in the form ax² + bx + c = 0 is given by the formula: D = b² - 4ac.
2. For the equation 2x² + kx + 3 = 0, the values of a, b, and c are: a = 2, b = k, and c = 3.
3. Since the equation has two equal roots, the discriminant (D) must be equal to zero.
4. Setting D = 0, we can now solve for k:
- D = b² - 4ac = k² - 4(2)(3) = k² - 24 = 0
5. Rearranging the equation, we have:
- k² = 24
6. Taking the square root of both sides, we find:
- k = ±√24
7. Simplifying the square root of 24, we get:
- k = ±√(4 * 6) = ±(2√6)
Therefore, the value of k that satisfies the condition of the equation having two equal roots is ±(2√6). So, the correct answer is (d) ±2√6.