Final answer:
The statement regarding polynomials with three terms being called trinomials is correct. Vectors can form the shape of a right angle triangle with their components. Dimensional consistency requires terms in an equation to correspond to the same unit or dimension.
Step-by-step explanation:
Polynomials that have exactly three terms are indeed called trinomials, which makes the student's statement (a) True. Trinomials can be easily recognized because they follow a specific pattern with three distinct terms, such as a general form ax2 + bx + c, where each term contributes to the overall expression.
Moreover, when breaking down the components of a vector, it is factual that a vector can form the shape of a right angle triangle with its x and y components. This is quite common in physics and mathematics when vectors are decomposed into perpendicular components, which aligns with the statement (b) as being True.
In mathematical equations, it is essential that all terms have the same dimension in order for the equation to be dimensionally consistent. This is achieved by ensuring each term when broken down, corresponds to the same unit or dimension. For instance, in the case of kinematic equations, the measurement units for terms involving displacement (s), velocity (v), time (t), and acceleration (a) need to be compatible, typically as a form of length (L) and time (T).
When analyzing quadratic equations, these are indeed a type of second-order polynomial or, more commonly, quadratic functions. A classic quadratic function has a trinomial form, where the highest power of the variable is two, denoted generally by ax2+bx+c.