Final answer:
The question asks about the Rational Root Theorem, which is applied in mathematics to determine the potential rational roots of a polynomial. The properties of square roots and their relation to exponents are also addressed, as well as the significance of real and positive roots in physical applications of quadratic equations.
Step-by-step explanation:
The student's question pertains to the Rational Root Theorem, which is a mathematical principle used to determine the potential rational roots of a polynomial equation. According to this theorem, if a polynomial has rational roots, they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. For the equation provided, f(x) = -6/5, -1/4, 3,6, the potential roots listed can be tested by substituting them into f(x) and checking if the result is zero.
In general, when working with radicals like square roots or cube roots, it is important to understand their properties and how they relate to exponents. For example, the square root of a number x is written as x² = √x, which is equivalent to the number raised to the 1/2 power. This concept is useful when solving equilibrium problems that may involve roots, as well as in manipulating and solving quadratic equations or expressions with exponents.
When dealing with physical data in the form of quadratic equations, it's crucial to keep in mind that only real roots are of interest, and within these, often the positive roots are the ones that make physical sense in a given context.