Final answer:
To find the values of k for which the quadratic equation has one real solution, consider the discriminant of the quadratic equation and set it equal to zero. The values of k can be expressed as the inequality k ≤ T²/8.
Step-by-step explanation:
To find the values of k for which the quadratic equation has one real solution, we need to consider the discriminant of the quadratic equation. The discriminant is the expression b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. In this case, the equation is 2x² + Tx + k = 0, so the discriminant is T² - 4(2)(k).
A quadratic equation has one real solution when the discriminant is equal to zero, so we set the discriminant equal to zero and solve for T: T² - 4(2)(k) = 0.
The solution is: T² = 8k. Therefore, the values of k for which the quadratic equation has one real solution can be expressed as the inequality k ≤ T²/8.