Final answer:
The expression for (F(x)) in terms of (x) is derived using the quadratic formula with the given values a = 3, b = 13, and c = -10. The discriminant is calculated, and the solutions are simplified, resulting in two potential expressions: −6 + √17 and −6 - √17.
Step-by-step explanation:
The expression for (F(x)) in terms of (x) appears to require the use of the quadratic formula based on the provided values a = 3, b = 13, and c = -10. To apply the quadratic formula, x = −b ± √(b² - 4ac)/(2a), we first calculate the discriminant, which is b² - 4ac. Plugging in our values, we get (13)² - 4 × 3 × (−10), which simplifies to 169 + 120, yielding 289. The square root of 289 is 17. Therefore, we substitute back into the quadratic formula to get −13 ± 17 over 2 × 3. This gives us two possible solutions: −6 + √17 and −6 - √17. When looking at the provided options for (F(x)), none appears to directly match this outcome, so further clarification might be needed from the student to determine the correct form of (F(x)).