Final answer:
The question is about finding rational roots of a fourth-degree polynomial equation. The solution involves using the quadratic formula if the polynomial can be factored into quadratic factors.
Step-by-step explanation:
The student is asking to find the rational roots of a polynomial equation, specifically x^4 + 3x^3 + 3x^2 - 3x - 4 = 0. To find the rational roots of a polynomial, we can use the Rational Root Theorem, which states that if a polynomial has rational roots, they are of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. However, the given equation is of the fourth degree, and the Rational Root Theorem does not provide a direct solution in this case. But for the quadratic equation ax^2 + bx + c = 0, the solution or roots can be calculated using the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a). If the polynomial can be factored into quadratic factors, each one can be solved using the quadratic formula.