The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) will have exactly \( n \) roots in the complex number system, counting multiplicities. Let's analyze each equation:
a. \( -9x + 4x^2 + 3 = 0 \) is a quadratic (degree 2) polynomial, which has 2 solutions (could be real or complex).
b. \( -2x^2 - 5 = 0 \) is also a quadratic (degree 2) polynomial. Thus, it has 2 solutions as well.
c. \( 57x^2 = 0 \) is again a quadratic (degree 2) but only has 1 unique solution (a double root at \( x = 0 \)).
d. \( 0x^2 + 7x - 2 = 0 \) simplifies to a linear equation (degree 1), which has 1 solution.
e. \( 0x^3 - x^2 + 2x + 4 = 0 \) simplifies to a quadratic (degree 2) polynomial, which has 2 solutions.
The equations that have two solutions are (a), (b), and (e).