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so -200
3-1 40 -199
3--81
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9
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66)
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, 4 t 2, t5, +, t10
).Rmts
- 0.438
- 4-S62
p. 264, FS) Sl1)
= a
+12a z k +p
t , t2, t5, 110
/2
2
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I
12 21
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34
t
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12 21 O
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2o
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x(41-2zds)=18
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2
4-2 4
4
2(2
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6633 1
22 12
,
)
O
Name Ane tmacr
Magnet Precale C
Rose
Complex Roots
1. f is a 5th degree polynomial with real coefficients
S(4-i) =0
S(2) = 0
Find the rule forf. (It's not necessary to multiply everything out.)
S(5+2i) =0
S(1) = 400
a--a-
tz-t+][z-(SIz:)](x-1)
1)=a-4)+][a -)-15)+2:]a-s)-2](z-)
S)=a ( - l2+l7)(-104+29)-2)
)=(10)(20)-1)= -200 40D> -2
(2= -2 (-iztl7(«-10at
Sx) x* +r* -15x +25
=
2.
2.
29)(z-)
Find the other roots of
S2-i) = 0
f)-2-i][2-(a+)]()
2 t ) z 3tu2-ISz+ 2S
2)= (z-4+5)Cu
)= (-va+)
-4
+S
OSx2-20
oos
7S
2.0LT2
2 t i , 2-i
-207x+26
3 fx)= x - x ' -32r +157x*
S3-2i)=0
Find the other roots off.
)-le-v2] Gr:)Jlz-("*2)||z-() m
z3+ 2
1-1'-n-31x' +Iu7A-2/7A
-C4/ 3a
S2-43TC
2
4.2,0'(A
2,=3+2
-2,
O-2-Ha+
-2-
*7-7
2
2
O
S + 2-202
O
22-L4
f(x)
=
g(x)+C
C--6) Ul1,ca)
5.
g
alx
1
2
nonrC
2 red
roots does g have?
How many real and how many nonreal
is a relative minimum
g(1)=2
are relative maxima
root",
-14x*
+
2 nonreal roots:
66x-104) and f(5-i)= 0.
-0-11)
4 nonreal roots:
1 real "double
-6,-2
2 distinct real roots, 1 real "double
root
1
g(8) =11
g-4.5) = 6 and
g(1) = 0
8(-7)=0
graphed below
forfif f)
=-102.
(,4
5-i) +S)+V,= 14
4S+i,Si
Poots
s(a) a(a-fib-r.)(2-) 1(7'-(17,1)x*+(or,
rule
2
Quickly, without doing any algebra or polynomial long division, what are the other roots of f? Give a
=
1
with real coeflicients,
fis a cubic equation with real coefficients. flx)
NIA
2 real "double roots":
4,-2)
4 distinct real roots:
T
willf have...
t11
t-10
2 distinct real roots, 2 nonreal:
For what values of c
Let
-11 -10 -9
degree polynominl
(4:5
Consider the 4h
N
LA
(
8. fis a cubie with real coefficients.
f2)= 0. f(4-i) = 0, and f(1) = 8
Find a rule forf.
ax-2Xz
-(4-)Xr -(44:))
)=a(z-2) ( 1-9z. 17)
a(-)10)= = - 10 = 9
(a)=-(n-2Yz
a-
-Sx+17
9. flx)= 3x -33x +99x-54
5-V13
= 0
Find the other roots
2
(
D)(1-E)-
off.
)
(-2)
7-Cx
3«-33xl
3a-
+49z-04
-1 4 90n-*
2
f)=0
19 - 4
=o
StT 6
2
4