Okay, let's solve this step-by-step:
We have the quadratic equation: 2x^2 + kx + 3 = 0
For the quadratic equation to have equal roots, the discriminant (b^2 - 4ac) must be equal to 0.
The discriminant for this equation is: (k^2 - 8*2*3) = k^2 - 48
Setting this equal to 0 and solving for k gives us:
k^2 - 48 = 0
k^2 = 48
k = +/- 6
Therefore, the values of k that give the equation two equal roots are:
k = +6 and k = -6