Math Problem Solver

Two functions, 𝑓 and 𝑔 are defined by

f(x) = 2x^5 - 54x^3 - 76x - 50; g(x) = 11x^4 - 244x^2 + 55.

Using a graphing software, generate the graphs of 𝑓 and 𝑔 on the same plane. Set the visible range of the x-axis to ±10 and that of the y-axis to ±3000. Use red and blue for the graph of 𝑓 and 𝑔 respectively. Use either labelling or legend to identify the graphs. Present the image, with a description that features number of roots and points of intersection. [4]

Using algebraic method(s) such as the factor theorem, determine all points of intersection of the graphs of 𝑓 and 𝑔. Are all these points shown on the graph? Present your detailed steps as your solution to this part.