Final answer:
The quartic polynomial equation 2x^4 - x^3 - 12x^2 - 25x + 5 = 0 has exactly 4 roots according to the Fundamental Theorem of Algebra. These roots can be real or complex and are the solutions that make the equation equal to zero.
Step-by-step explanation:
The given equation, 2x4 - x3 - 12x2 - 25x + 5 = 0, is a polynomial equation of the fourth degree (also known as a quartic equation), which means it has 4 roots. A fundamental principle of algebra, known as the Fundamental Theorem of Algebra, states that every non-zero, single-variable, degree n polynomial with complex coefficients has exactly n roots in the complex number system. Thus, our equation will have 4 roots that can be real or complex. These roots are the solutions to the equation that make it equal to zero. To find these roots, one would typically use numerical methods or factoring techniques if applicable, but the precise root values are not provided here.