Yes, because of complex-not real-solutions. For instance, if it has two real roots or x-intercepts and two complex conjugate roots, it then possesses four solutions and it will cross the x-axis only twice.

You're describing the nature of the roots of a polynomial function, particularly a quadratic or higher-degree polynomial. In the case of a quadratic function, the number of real and complex roots can be determined by the discriminant (\(D = b^2 - 4ac\)).

1. Two Real Roots: If the discriminant is greater than zero (\(D > 0\)), the polynomial has two distinct real roots. This means it will cross the x-axis at two points.

2. Complex Conjugate Roots: If the discriminant is less than zero (\(D < 0\)), the polynomial has two complex conjugate roots. These roots do not correspond to any points where the graph intersects the x-axis.

3. One Real Root: If the discriminant is equal to zero (\(D = 0\)), the polynomial has one real root, also referred to as a repeated or double root. In this case, the graph will just touch the x-axis at this point but not cross it.

For higher-degree polynomials, the same concepts apply but can be more complex. A polynomial of degree \(n\) will always have \(n\) roots, counting multiplicities, according to the Fundamental Theorem of Algebra. If there are \(r\) real roots, then \(n - r\) will be the number of complex roots, which will occur in conjugate pairs.

In your example, if a polynomial has two real roots and two complex conjugate roots, it indicates that it is a fourth-degree polynomial. The graph will cross the x-axis at the two real roots and will not touch or cross the x-axis at all since there are no additional real roots. Thus, it visually represents the concept of having both real and complex solutions effectively.