Final answer:
The student's question seems to relate to a quadratic equation, but they did not provide sufficient context or details to accurately determine the value of c. The symbols RS, RT, and ST appear to be segments that could relate to a geometry problem involving algebra. More information is required to solve the problem.
Step-by-step explanation:
The student provided a question that seems to involve segments and algebra, but the student didn't give enough context to determine the exact question about the value of c. However, they did mention an equation of the form at² + bt + c = 0, which is a quadratic equation. Solving a quadratic equation typically involves determining the constants a, b, and c and then applying the quadratic formula.
The question provides several equations: RS = 3x + 5, RT = 8x, ST = 3x + 1, but without further information on how these are related to each other or to the quadratic equation, we cannot determine the value of c. If the student intended to find the value of c from a given quadratic equation, more information or clarity is needed to proceed.