Final answer:
The necessary information to calculate tan(b) is not provided. The angle b and its trigonometric context such as a right triangle or a function on the unit circle are required to find the tangent value.
Step-by-step explanation:
The question is asking to find the value of tan(b), which is the tangent of angle b. The options given are 4/3, 3/4, 4/5, and 3/5. However, the information provided in the background like the quadratic equation, its solutions, and other challenge problems do not directly supply the necessary trigonometric details to calculate tan(b). To find the tangent of an angle, one would typically use a right triangle or a unit circle, and the value would depend on the specific angle b.
Since we do not have enough context to determine the value of tan(b) for this question, we recommend the student review the original problem statement for a diagram or additional information that might have been omitted, which is crucial to solve for tan(b).