Final answer:
The question involves solving a quadratic equation using the quadratic formula. The constants a, b, and c are substituted into the formula to find the solutions, which are the roots of the equation.
Step-by-step explanation:
The student's question relates to the solutions of a quadratic equation in the form at² + bt + c = 0, where a, b, and c are constants. To solve for the variable t, we use the quadratic formula, which is t = (-b ± √(b²-4ac))/(2a).
When the constants are given, such as a = 1.00, b = 10.0, and c = -200, we can substitute these values into the quadratic formula to find the solutions for t. These solutions will be the points where the quadratic equation crosses the t-axis, representing the roots of the equation.
For example, substituting a = 4.90, b = -14.3, and c = -20.0 into the quadratic formula, we can find the two possible solutions for t, which can be positive, negative, or complex numbers depending on the discriminant b²-4ac.