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Unformatted text preview: NAME (Printed) 11341: MATH 118
EXAM 2
August 19, 2002
Professor Borzellino Instructions: Read each question care
fully and answer it in the space provided. Calculators, books and notes are not to
be used. Read through the entire exam before he
g‘inning work. There are a total of 6 ques—
tions on 6 pages, not counting this page. Question 1 [20 points] Consider the polynomial P(r1:) : 2:4 — 36. a) Factor the polynomial completely over 1R into linear factors and irreducible quadratic
factors. 7  ax" , Kira}
5x34; 13) List all real roots of P(.'I:).
X21” c) Factor the polynomial completely over (C into linear factors. * O
)5 ‘“ “i” ') l: (1) List all complex roots of P(:I;). trim? \/
if 19‘ Question 2 [10 points] a) For what value of B will the function f(::r:) : 2.1:2 +3.7; — 5
have a minimum at :1: = 3? 3 Question 3 [20 points] Sarah invests $1000 in government bonds. Assume the bonds
yield 6% annual interest. a) Write a formula for the value of her investment afte‘ at years assuming interest compounded monthly.
1L ‘ 115,".va + b) Write a formula for the value of her investment after t years assuming interest is
compounded continuously. ' [issues.11; «MUM ‘1 {Rio r m! L cl'How long will it take before the value of her investment reaches $5000? J .t 5:50“ unsweer ‘ RPM» :— d) SkEtCh the g1" aph 0f y = Tm” 0n the axes below. Label the y—intercept. Question 4 [20 points] 3.) Find a polynomial with real coefﬁcients of degree 4
that has roots :1: = 1, 2 and 1 + 225 KXJ) “1300 (\Jr2',))(x+(\+aw)) ()(lngwzl Macaw2" ) xz—si via“am
. Kl ‘35” +Z><LFS¢Z +\$>t— \O \. j? b) Give an example of a polynomial with real coefﬁcients of degree 4 that has
no real roots. Explain. It might be easier to represent your polynomial in factored form.
2. .
3:
1L 6
s 1 S
0) Use the rational root theorem to factor completely 3:3 — 5:1:2 + 2:1: — 10.
\25«12g+Iol0 i}’ta‘t:3¢ IO
>z?+Z ig<~6ibé3+23 "3
K‘ S \l 7‘31 53L2' 1'“c:DL— 1C) c___..__.__.—————‘M
‘ 7( +3? ” Z_ i 7
£241.19. Mm":
T" '“‘\
5 $105..
. . 1 + i . . . . .
d) Simplify the complex number 2, by writing 1t 1n the form a + bx.
"'" 19 MB L3» 2") 3+3'w2x ,_. I +31 ". "
27323 1 +Li [L502 lel‘VBﬁZ‘i’ol 01 Question 5 [20 points] Suppose that the function 19 2 —%rr: + 200 relates the selling
price of p of a Calculus book to the number of books .7; that are sold. a) Find a function that represents the total revenue from selling .1: books. Re— member total revenue 2 (price)1(quantity sold) .qu , r __d
thbﬁ 31‘ v‘ —‘ f1 + Edi—(3 A
126%) =— ""l/sycl+2a~x>,< b) How many books should be sold to generate maximum revenue? _ __ —— 20C”)
. A E _ _ a; 33; ~—1
i :5 J}  4:00 . i I, .‘
“~92 Vi) ' :3 c) What price should the books he sold to generate maximum revenue? F) 3 ‘VSC&M)+ZDO  l Go 4 ;> o 0/ F: 10 O
45 me Rosie .~. ‘15 xﬁ‘zoo; » {.71 l 3) Proﬁt = “wheel +5 4/3 L: 4‘ Question 6 [10 points] Solve the equations:
a) 84x9+2m 2 «E “Z 6
__\___
Wk" “2 \L» V3 "‘1
.u. 2409.
\ L..
3 he ii I “T
235 Jq——c4(q)(~\zz.\ ﬂziﬁTﬁf ...
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 Math, Complex number, real roots, linear factors, real coefficients

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