11/18/13
Theorems About Roots of Polynomial Equations
Theorems About Roots of Polynomial Equations
Melanie Bellido Puna is reviewing answers for this assessment.
Points scored may differ from the grading guidelines because of teacher review. Contact your program
teacher if you have any questions.
Correct
Partial Credit
Incorrect
Multiple Choice
1. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x3 – x2 – x
– 3 = 0. Do not find the actual roots. (1 point)
(1
(0
(0
(0
pt) –3, –1, 1, 3
pts) 1, 3
pts) –33
pts) no roots
1 /1 point
This item has been reviewed and is scheduled to be updated. All students will receive full credit for
any response to the following.
2. Find the roots of the polynomial equation.
2x3 + 2x2 – 19x + 20 = 0 (1 point)
(1 pt)
,
, –4
(1 pt)
,
,4
(1 pt)
,
, –4
(1 pt)
,
,4
1 /1 point
3. A cubic polynomial with rational coefficients has the roots 6 +
and
. Find one additional root.
(1 point)
(0 pts) –6 –
(0 pts) 6 +
(0 pts) –6 +
(1 pt) 6 –
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11/18/13
Theorems About Roots of Polynomial Equations
1 /1 point
4. Find a third-degree polynomial equation with rational coefficients that has roots –4 and 6 + i.
(1 point)
(1 pt) x3 – 8x2 – 11x + 148 = 0
(0 pts) x3 – 8x2 – 12x + 37 = 0
(0 pts) x3 – 12x2 + 37x = 0
(0 pts) x3 – 8x2 – 11x = 0
1 /1 point
5. What does Descartes's Rule of Signs tell you about the real roots of the polynomial?
–2x3 + 3x2 – 5x – 2 = 0 (1 point)
(0
(0
(0
(1
pts) There is one positive root and either 2 or 0 negative roots.
pts) There are either 2 or 0 positive roots and there are either 2 or 0 negative roots.
pts) There is one positive root and one negative root.
pt) There are either 2 or 0 positive roots and one negative root.
1 /1 point
The final score is 5/5 (100%).
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