Math 1650 Section 622
(old) Exam number 2
Show all work. How you get your answer is just
as important, if not more important, than the
answer itself. If you think it, write it!
- 6.
-
(8 pts. each) For the polynomial function
f(x) = x4-3x2+4x-6
use (synthetic or polynomial long) division to write f(x) as
(a) (x-2)g(x)+c
(b) (x+1)h(x)+d
- 1.
-
(12 pts.) Show that the polynomial
f(x) = x5+3x3-x2-4
has only one real root. (Hint: think positive vs. negative roots). What two consecutive
integers does it lie between?
- 2.
-
(12 pts.) Find all of the rational roots of the polynomial
f(x) = 2x3-13x2+3
- 3.
-
(12 pts.) One root of the function
f(x) = 2x4-5x3+5x2-2
is 1+i (you DON'T need to check this!). Find all of the other roots.
- 4.
-
(6 pts. each) Find the following numbers (write them in standard form):
(a): (1+Ö2i)(1-3i) =
(b): [(1+Ö2i)/(1-3i)] =
- 5.
-
(15 pts.) Find all of the relevant asymptotes of the function
f(x) = [(3x2)/(x+2)]
and use this information to help draw a graph of the function.
- 6.
-
(10 pts.) Use the rules of logarithms to expand the following
expression as much as possible:
log4([((x2+1)3/2x32)/((x-3)4)])
- 7.
-
(12 pts.) Solve for x:
ln(x+1)-2ln(x) = 0
- 8.
-
(15 pts.) How long will it take your money to triple if it is invested at
12% interest, compounded 4 times per year? (You may leave your answer in terms of
logs.)
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