- If the discriminant in a quadratic equation is a negative real number, it means that
(a) the equation has two different real roots.
(b) the equation has one real root with multiplicity 2.
(c) the equation has one imaginary root with multiplicity 2.
(d) the equation has two different imaginary or complex roots.
(e) the equation has no roots at all, real or complex.
- A mapping is a bijection if and only if it is
(a) reflexive.
(b) a function.
(c) one-to-one and onto.
(d) a subset of its co-domain.
(e) transitive.
- Consider the following pair of equations as a two-by-two system:
y=a 1 x+b 1
and
y=a 2 x+b 2
where a 1 ,a 2 ,b 1 , and b 2 are real numbers, and neither a 1 nor a 2 are equal to 0. What
are the smallest and largest numbers of elements that the solution set of such a system
can have? Assume that the two equations are not identical, and are not some constant
multiple of each other.
(a) None, and one.
(b) None, and two.
(c) None, and infinitely many.
(d) One, and infinitely many.
(e) Two, and infinitely many.
Final Exam 585
