Final answer:
The value of k for which the equation 2x^2 - 6x + k = 0 has exactly one solution is 4.5, found by setting the discriminant of the quadratic equation to zero.
Step-by-step explanation:
For the equation 2x2 - 6x + k = 0 to have exactly one solution, the discriminant of the quadratic equation must be zero. The discriminant is given by the formula b2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax2 + bx + c. In this equation, a = 2, b = -6, and c = k. Plugging in the values, we get (-6)2 - 4(2)(k) = 0. Simplifying, we find that 36 - 8k = 0. Solving for k, we find that k must be 4.5 for the equation to have exactly one solution.