580 Final Exam
(d) one solution is an ordered pair of reals, and the other solution is an ordered pair of
pure imaginary numbers.
(e) both solutions are ordered pairs of complex (but not real) numbers.- If a number decreases by a factor of 100, then its natural logarithm
(a) decreases by a factor of ln 100, or approximately 4.6.
(b) decreases by a factor of exactly 2.
(c) increases by a factor of exactly 2.
(d) increases by a factor of ln 100, or approximately 4.6.
(e) increases by a factor of the square root of 100, or exactly 10. - Which of the following statements concerning natural numbers is false?
(a) A number must be either even or odd, but can’t be both.
(b) An even number plus 1 is always odd.
(c) An even number divided by 2 is always a natural number.
(d) An odd number times 2 is always a natural number.
(e) An odd number divided by 2 is always a natural number. - Suppose we want to solve a higher-degree polynomial equation, and we’re told that
all the roots are irrational numbers. What can we do to find, or at least approximate,
those roots?
(a) We can factor the equation into the nth power of a binomial (where n is the
degree of the equation), make that binomial into a first-degree equation, and then
solve that equation.
(b) We can factor the equation into the nth power of a trinomial (where n is the
degree of the equation), make that trinomial into a quadratic, and then solve that
equation with the quadratic formula.
(c) We can factor the equation into binomials with integer coefficients and integer
constants, and then derive the roots from those binomials.
(d) We can use synthetic division to find the upper and lower bounds of the real
roots, and then find those roots using the rational roots theorem.
(e) We can use a computer program to graph the function produced by the
polynomial, and then use the computer to approximate the zeros of that
function. - If a number increases by a factor of 10,000, then its common logarithm
(a) decreases by a factor of ln 10,000, or approximately 9.2.
(b) decreases by a factor of exactly 4.
(c) increases by a factor of exactly 4.
(d) increases by a factor of ln 10,000, or approximately 9.2.
(e) increases by a factor of the square root of 10,000, or exactly 100. - Figure FE-14 shows the graphs of two quadratic functions in a real-number
rectangular coordinate plane. The origin (0, 0) is where the x and y axes intersect. The