The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) will have exactly \( n \) roots, counted with multiplicity. To determine which equations have two solutions, we need to assess the degree of each polynomial:
a. The equation \(-9x + 4x^2 + 3 = 0\) is a quadratic equation (degree 2) and has two solutions.
b. The equation \(-2x^2 - 5 = 0\) is also a quadratic (degree 2) and will have two solutions.
c. The equation \(57x^2 = 0\) is again quadratic, but it gives a double root at \(x = 0\), counting as one unique solution.
d. The equation \(0x^2 + 7x - 2 = 0\) simplifies to \(7x - 2 = 0\), which is linear (degree 1) and has one solution.
e. The equation \(0x^3 - x^2 + 2x + 4 = 0\) simplifies to \(-x^2 + 2x + 4 = 0\), which is also quadratic (degree 2) and will have two solutions.
Thus, the equations with two solutions are (a), (b), and (e).