Final answer:
The function f(x) = 3x^5 + 30x^4 + 35x^4 simplifies to f(x) = 33x^5 + 35x^4. Factoring out x^4, we find one root at x = 0 with a multiplicity of 4 and another root from the factor (33x + 35). Therefore, there are five zeros in total.
Step-by-step explanation:
The question regarding the zeros of the function f(x) = 3x^5 + 30x^4 + 35x^4 is a question about finding the solutions to the equation f(x) = 0, which represent the x-intercepts, or zeros, of the graph of the function. By combining like terms, we simplify the function to f(x) = 33x^5 + 35x^4. Both terms contain a factor of x, so we can factor out x^4 to get x^4(33x + 35). This leaves us with one factor, x^4, which gives us a root at x = 0 with a multiplicity of 4, and the second factor, (33x + 35), giving us another root. Thus, the correct answer is d) There are five zeros.