analyzing and solving polynomial equations
TRANSCRIPT
8/12/2019 Analyzing and Solving Polynomial Equations
http://slidepdf.com/reader/full/analyzing-and-solving-polynomial-equations 1/4
5KSuHtRa9 qSTo4f Pt gwIaBrheo WLLLxC9.8 s JAIlElG Krri4gBh9t9sq HrpensLeyrbvHeDdO.3 t 5MlavdGey ZwsiatJhc CI8nbf 2iPnYimtsez VAhl4gJe6bqrcak i2Q.U Worksheet by Kut
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Analyzing and Solving Polynomial Equations
State the number of complex roots, the possible number of real and imaginary roots, the possible
number of positive and negative roots, and the possible rational roots for each equation. Then find all
roots.
1) x4 − 5 x
2 − 36 = 0 2) x
3 + 3 x
2 − 14 x − 20 = 0
3) x3 − 2 x
2 + 3 x − 6 = 0 4) x
4 − 14 x
2 + 45 = 0
5) x4 + 6 x
2 + 8 = 0 6) x
4 + 3 x
2 − 18 = 0
7) x3 − 1 = 0 8) x
3 + 3 x
2 − x − 3 = 0
-1-
8/12/2019 Analyzing and Solving Polynomial Equations
http://slidepdf.com/reader/full/analyzing-and-solving-polynomial-equations 2/4
lK ju3t9aL BS5oRf etUwEaxrpeU XL0LJCB.E V CAulZlF br4iTgCh9tNsU yrPemsAeBrVv jeKd8.L w EMRaFdgeu TwmiHt0hZ HIAnxf PiUnxiptwee 5AulbgDelbvrbae k2g.B Worksheet by Kut
9) x3 − 2 x
2 − 3 x + 6 = 0 10) x
6 − 2 x
4 − 4 x
2 + 8 = 0
11) x5 + 2 x
4 + 11 x
3 + 22 x
2 + 24 x + 48 = 0 12) x
6 + 5 x
4 − 4 x
2 − 20 = 0
13) x6 − x
4 − x
2 + 1 = 0 14) x
8 − 26 x
4 + 25 = 0
-2-
8/12/2019 Analyzing and Solving Polynomial Equations
http://slidepdf.com/reader/full/analyzing-and-solving-polynomial-equations 3/4
pK5uTtnaS xSVoOf Tt7wta8rAeh nLzLECm.3 B 2ANl7ls irVingGhVt Isw 5rVeYs8eJrFv6eUdX.Z V WMkahdTeO RwzixtZhr II4nqf Qi1nDiAt zeW JAVlkg jetbBrVaw m2a.z Worksheet by Kut
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________Analyzing and Solving Polynomial Equations
State the number of complex roots, the possible number of real and imaginary roots, the possible
number of positive and negative roots, and the possible rational roots for each equation. Then find all
roots.
1) x4 − 5 x
2 − 36 = 0
# of complex roots: 4
Possible # of real roots: 4, 2, or 0
Possible # of imaginary roots: 4, 2, or 0
Possible # positive real roots: 1
Possible # negative real roots: 1
Possible rational roots:
± 1, ± 2, ± 3, ± 4, ± 6, ± 9, ± 12, ± 18, ± 36
Roots: {2i, −2i, 3, −3}
2) x3 + 3 x
2 − 14 x − 20 = 0
# of complex roots: 3
Possible # of real roots: 3 or 1
Possible # of imaginary roots: 2 or 0
Possible # positive real roots: 1
Possible # negative real roots: 2 or 0
Possible rational roots:
± 1, ± 2, ± 4, ± 5, ± 10, ± 20
Roots: {−5, 1 + 5 , 1 − 5}
3) x3 − 2 x
2 + 3 x − 6 = 0
# of complex roots: 3Possible # of real roots: 3 or 1
Possible # of imaginary roots: 2 or 0
Possible # positive real roots: 3 or 1
Possible # negative real roots: 0
Possible rational roots: ± 1, ± 2, ± 3, ± 6
Roots: {2, i 3, −i 3}
4) x4 − 14 x
2 + 45 = 0
# of complex roots: 4Possible # of real roots: 4, 2, or 0
Possible # of imaginary roots: 4, 2, or 0
Possible # positive real roots: 2 or 0
Possible # negative real roots: 2 or 0
Possible rational roots:
± 1, ± 3, ± 5, ± 9, ± 15, ± 45
Roots: { 5, − 5, 3, −3}
5) x4 + 6 x
2 + 8 = 0
# of complex roots: 4Possible # of real roots: 4, 2, or 0
Possible # of imaginary roots: 4, 2, or 0
Possible # positive real roots: 0
Possible # negative real roots: 0
Possible rational roots: ± 1, ± 2, ± 4, ± 8
Roots: {2i, −2i, i 2, −i 2}
6) x4 + 3 x
2 − 18 = 0
# of complex roots: 4Possible # of real roots: 4, 2, or 0
Possible # of imaginary roots: 4, 2, or 0
Possible # positive real roots: 1
Possible # negative real roots: 1
Possible rational roots: ± 1, ± 2, ± 3, ± 6, ± 9, ± 18
Roots: { 3, − 3, i 6, −i 6}
7) x3 − 1 = 0
# of complex roots: 3
Possible # of real roots: 3 or 1
Possible # of imaginary roots: 2 or 0
Possible # positive real roots: 1
Possible # negative real roots: 0
Possible rational roots: ± 1
Roots: {1,−1 + i 3
2,
−1 − i 3
2 }
8) x3 + 3 x
2 − x − 3 = 0
# of complex roots: 3Possible # of real roots: 3 or 1
Possible # of imaginary roots: 2 or 0
Possible # positive real roots: 1
Possible # negative real roots: 2 or 0
Possible rational roots: ± 1, ± 3
Roots: {−3, 1, −1}
-1-
8/12/2019 Analyzing and Solving Polynomial Equations
http://slidepdf.com/reader/full/analyzing-and-solving-polynomial-equations 4/4
9) x3 − 2 x
2 − 3 x + 6 = 0
# of complex roots: 3
Possible # of real roots: 3 or 1
Possible # of imaginary roots: 2 or 0
Possible # positive real roots: 2 or 0
Possible # negative real roots: 1
Possible rational roots: ± 1, ± 2, ± 3, ± 6
Roots: {2,
3,
− 3
}
10) x6 − 2 x
4 − 4 x
2 + 8 = 0
# of complex roots: 6
Possible # of real roots: 6, 4, 2, or 0
Possible # of imaginary roots: 6, 4, 2, or 0
Possible # positive real roots: 2 or 0
Possible # negative real roots: 2 or 0
Possible rational roots: ± 1, ± 2, ± 4, ± 8
Roots: {2
mult. 2,− 2
mult. 2,i 2
,−i 2
}
11) x5 + 2 x
4 + 11 x
3 + 22 x
2 + 24 x + 48 = 0
# of complex roots: 5
Possible # of real roots: 5, 3, or 1
Possible # of imaginary roots: 4, 2, or 0
Possible # positive real roots: 0
Possible # negative real roots: 5, 3, or 1
Possible rational roots:
± 1, ± 2, ± 3, ± 4, ± 6, ± 8, ± 12, ± 16, ± 24, ± 48
Roots: {−2, i 3, −i 3, 2i 2, −2i 2}
12) x6 + 5 x
4 − 4 x
2 − 20 = 0
# of complex roots: 6
Possible # of real roots: 6, 4, 2, or 0
Possible # of imaginary roots: 6, 4, 2, or 0
Possible # positive real roots: 1
Possible # negative real roots: 1
Possible rational roots:
± 1, ± 2, ± 4, ± 5, ± 10, ± 20
Roots: {i 5, −i 5, 2, − 2, i 2, −i 2}
13) x6 − x
4 − x
2 + 1 = 0
# of complex roots: 6
Possible # of real roots: 6, 4, 2, or 0
Possible # of imaginary roots: 6, 4, 2, or 0
Possible # positive real roots: 2 or 0
Possible # negative real roots: 2 or 0
Possible rational roots: ± 1
Roots: {1 mult. 2, −1 mult. 2, i, −i}
14) x8 − 26 x
4 + 25 = 0
# of complex roots: 8
Possible # of real roots: 8, 6, 4, 2, or 0
Possible # of imaginary roots: 8, 6, 4, 2, or 0
Possible # positive real roots: 2 or 0
Possible # negative real roots: 2 or 0
Possible rational roots: ± 1, ± 5, ± 25
Roots: {1, −1, i, −i, 5 , − 5, i 5, −i 5}
2
Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com