Post on 26-Mar-2015
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Remainder & Factor
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Finding Rational
Roots100 100 100
200 200 200
300 300 300
400 400 400
500 500 500
Is x+1 a factor of x15-3x-2
Yes
Accord. To Descartes Rule, what is the
possible # of positive roots of x3-2x2-5=0
1 Possible
List the possible rational roots of
4x4+3x2-1=0
± 1 , ± 2, ± 1/4
Find a poly. Whose roots are 0 and -1 d.r.
X3+2x2+x
Accord. To Descartes Rule, what is the
possible # of negative roots of x3-2x2-5=0
0 Negative
Solve over the real #’s x3-7x-6=0
(-1, -2, 3)
Solve 2y3-5y2-4y+3 with root 3
3,-1,1/2
Find a cubric eq. w/ R coffs. That has the roots
-1, 3-I
X3-5x2+4x+10=0
Solve over the complex #’s 4x4-4x3+5x2-
4x+1=0
1/2 (d.r.), ± i
Solve x4-x3-2x-4=0 with root
(±i, , -1, 2/3)
Find the remaining roots of x4+x3+6x2-14x-
20=0
-1 -3i ,-1
Solve over the Real #’s 2x3+x2-6x-3-x4+2x3-
2x2+18=0
Solve 3x4-5x3-7x2+3x+2=0
(1± , -1, 2/3)
Solve x4+12x-5=0
(1±2i, -1 ±
Solve over the complex #’s 6x4+x3+23x2+4x-
4=0
1/3, -1/2, ± 2i
Finding Rational
Roots
Answer page
Reminder and Factor
Thrm.
More Thrms. And
Rules.
2i
72
2 2
3,2
1
Is x+1 a factor of x15 - 3x – 2 ?
C1 – 100
Topic 1 – 100 / AnswerTopic 1 – 100 / Answer
Correct Question
C1-100 Q
Topic 1- 100 / QuestionTopic 1- 100 / Question
What is yes
Find a polynomial
whose roots are 0 and -1 double
root
C1 - 200
Topic 1 – 200 / AnswerTopic 1 – 200 / Answer
Correct Question
x3 + 2x2 + x
C1-200 Q
What is
Topic 1- 200 / QuestionTopic 1- 200 / Question
Solve
2y3 – 5y2 – 4y + 3
with root 3
C1 - 300
Topic 1 – 300 / AnswerTopic 1 – 300 / Answer
Correct Question
C1-300 Q
What is 3,-1, ½
Topic 1- 300 / QuestionTopic 1- 300 / Question
Solve
x4 – x3 – 2x – 4 = 0
with root
C1 - 400
Topic 1 – 400 / AnswerTopic 1 – 400 / Answer
Correct Question
2i
C1-400 Q
What are -1,2,
Topic 1- 400 / QuestionTopic 1- 400 / Question
2i
Solve
3x4–5x3–7x2+3x+2=0
given root
C1 - 500
Topic 1 – 500 / AnswerTopic 1 – 500 / Answer
Correct Question
21
C1-500 Q
What are , -1, 2/3
Topic 1- 500 / QuestionTopic 1- 500 / Question
21
According to Descartes’ Rule, what is the possible # of positive roots of
x3-2x2-5=0
C2 - 100
Topic 2 – 100 / AnswerTopic 2 – 100 / Answer
Correct Question
C2-100 Q
What is 1 positive
Topic 2- 100 / QuestionTopic 2- 100 / Question
According to Descartes’ Rule, what is the possible # of negative roots of
x3-2x2-5=0
C2 - 200
Topic 2 – 200 / Topic 2 – 200 / AnswerAnswer
Correct Question
C2-200 Q
What is 0 negative roots
Topic 2- 200 / QuestionTopic 2- 200 / Question
Find a cubic equation with real coefficients that has the roots -1 and 3-i.
C2 – 300
Topic 2 – 300 / AnswerTopic 2 – 300 / Answer
Correct Question
C2-300 Q
What is x3-5x2+4x+10=0
Topic 2- 300 / QuestionTopic 2- 300 / Question
Find the remaining roots of
x4+x3+6x2-14x-20=0 given its roots
2 and -1+3i
C2 - 400
Topic 2 – 400 / AnswerTopic 2 – 400 / AnswerCorrect Question
C2-400 Q
What are -1-3i and -1
Topic 2- 400 / QuestionTopic 2- 400 / Question
Solve x4+12x-5=0 given 1-2i is a root.
C2 - 500
Topic 2 – 500 / AnswerTopic 2 – 500 / Answer
Correct Question
C2-500 Q
What are
Topic 2- 500 / QuestionTopic 2- 500 / Question
2121 ,i
List the possible rational roots of 4x4 + 3x2 – 1 = 0
C3 - 100
Topic 3 – 100 / AnswerTopic 3 – 100 / Answer
Correct Question
C3-100 Q
What is
Topic 3- 100 / QuestionTopic 3- 100 / Question
4
1
2
11 ,,
Solve over the Real numbers:
x3 – 7x – 6 = 0
C3 - 200
Topic 3 – 200 / AnswerTopic 3 – 200 / Answer
Correct Question
C3-200Q
Topic 3- 200 / QuestionTopic 3- 200 / Question
What are-1,-2,3
C3 - 300
Topic 3 – 300 / AnswerTopic 3 – 300 / AnswerCorrect Question
Solve over the complex numbers:
4x4-4x3+5x2-4x+1=0
What are ½ d.r., i,-i
C3-300Q
Topic 3- 300 / QuestionTopic 3- 300 / Question
Solve over the
complex numbers:
2x3 + x2 - 6x – 3 =0
C3 - 400
Topic 3 – 400 / AnswerTopic 3 – 400 / Answer
Correct Question
C3-400Q
Topic 3- 400 / QuestionTopic 3- 400 / Question
What are
-1/2, 3
C3 - 500
Topic 3 – 500 / AnswerTopic 3 – 500 / Answer
Correct Question
Solve over the complex numbers:
6x4+x3+23x2+4x-4=0
C3-500Q
Topic 3- 500 / QuestionTopic 3- 500 / Question
What is
2
12
3
1 ,, i
POD