I need help on these pls, the answer choices are, Algebra, Reciprocal, Quotient, Pythagorean

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Which of the following quartic functions has x = –1 and x = –2 as its only two real zeroes?

Find the value of x for which line a is parallel to line b