Final answer:
The statement regarding the absolute value of a real number is true, as it always results in a non-negative number, which is particularly relevant in applications involving physical data where only positive roots may have real-world significance.
Step-by-step explanation:
The statement that the absolute value of any real number x is the non-negative value of x without regard to its sign is True. The absolute value of a number is denoted by two vertical lines |x|, which essentially erases any negative sign of the number, making it non-negative. For example, if x is a positive number, then |x| = x, and if x is negative, |x| = -x which then produces a positive result. This means, regardless of whether x is positive or negative, the absolute value |x| will ensure that the result is a non-negative number. When dealing with quadratic equations, especially those constructed on physical data, real roots are usually obtained, and only the positive values among these may be significant, since they can represent things like distances or concentrations which cannot be negative in the real world.
For instance, when solving a quadratic equation, you might get two solutions for x, such as x = 0.0216 or x = -0.0224. In certain contexts, such as measuring a physical quantity that cannot be negative, the negative solution would be discarded as it has no real-world significance, leaving the positive value of x as the likely solution.