For which values of k does the quadratic equation 2x^2+kx+3=0 only have one unique solution?

A quadratic equation ax² +bx+c=0 will have only one unique solution if and only if b²-4ac=0. If we apply this to the equation in the question, we get that k²-24=0. If we solve this equation we get two solutions : k = -24^1/2 or k=24^1/2. These are the values of k for which the quadratic equation 2x² +kx+3=0 has only one solution.