Final answer:
An accurate solution requires the correct value of 'c' to apply the quadratic formula. Without 'c', the given values of a and b (-9 and -4 respectively) cannot lead to a complete solution. The quadratic formula is correctly applied with well-defined values as illustrated in an example.
Step-by-step explanation:
The student's question pertains to substituting values into the quadratic formula to find the roots of a quadratic equation. Without the full context or the correct question, it is unclear which values should be used, as there is mention of both a = -9, b = -4 and other sets of values. Assuming the correct values are a = -9 and b = -4, the quadratic formula used to find the roots of the equation at² + bt + c = 0 is:
x = −b ± √(b² − 4ac) / (2a)
However, to proceed with finding the roots, the correct value of 'c' is required, which is not provided in the question. If 'c' was intended to be the item labeled 'C. -108, -4/3', it seems there might be a misunderstanding, as those look like potential answers, not the value of 'c'.
For a well-defined quadratic equation and corresponding values for a, b, and c, the roots can be calculated as shown in the following example:
For a quadratic equation where a = 3, b = 13, c = -10, the quadratic formula would yield:
x = −13 ± √((13)² − 4 × 3 × (−10)) / (2 × 3)
This simplifies to two potential solutions for x:
x = (-13 + √(169 + 120)) / 6
x = (-13 − √(169 + 120)) / 6
Further simplifying would provide the numerical values for the roots of the equation.