(c) Only if the variable can never become negative.
(d) Only if the variable can never become irrational.
(e) Always.
- Completing the square is a method of solving a quadratic equation for real roots by
(a) squaring the left and right sides.
(b) adding a constant to both sides in order to get the square root of a binomial on
one side and a positive real number on the other side.
(c) adding a constant to both sides in order to get the square of a binomial on one
side and a positive real number on the other side.
(d) taking the square root of both sides, discovering the imaginary roots if any exist.
(e) converting it into a cubic equation that turns out to be easier to solve than the
original quadratic.
- Which of the following statements is false?
(a) If a real number k is a root of a cubic equation in the variable x, then (x+k) is a
factor of the cubic polynomial.
(b) If a real number k is a root of a cubic equation in the variable x, then (x−k) is a
factor of the cubic polynomial.
(c) If k is a real number and (x−k) is a factor of a cubic polynomial in the variable x,
thenk is a real root of the cubic equation.
(d) All cubic equations have at least one real root, as long as the coefficients and the
stand-alone constant are all real numbers.
(e) A cubic equation can have one real root and two other roots that are complex
conjugates of each other.
- A mapping in which each element in the domain corresponds to one, but only one,
element in the range is called
(a) a rejection.
(b) a bijection.
(c) an injection.
(d) a surjection.
(e) onto.
- Consider the following quadratic equation in binomial factor form:
(x−j3)(x+j3)= 0
What is the solution set X for this equation?
(a)X= {3}
(b)X= {j3}
(c)X= {−3}
(d)X= {−j3}
(e) None of the above
Final Exam 561
