Step-by-step explanation:
To determine the number of solutions or zeros for the function \( f(x) = 3x^4 - 2x^2 + 3x - 2 \), we can use the concept of the fundamental theorem of algebra.
This polynomial is a quartic equation (\(3x^4 - 2x^2 + 3x - 2\)), which means it is a fourth-degree polynomial. According to the fundamental theorem of algebra, a polynomial of degree \(n\) has exactly \(n\) complex roots, counting multiplicities.
In this case, a quartic equation can have up to four solutions (real and/or complex) considering multiplicity. However, to precisely determine the number of real roots or zeros, further analysis, such as graphing the function or using calculus methods to find critical points, is needed.
We can't directly determine the exact number of real solutions or zeros without further analysis or context. The number of real roots can be zero, two, or four, depending on the nature of the function's graph and the values of its coefficients.
