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Question 594419: 1. Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first.
A.
B.
C.
D.
2. Solve 2x = 5x2 for x.
A. 2.322
B. 0 and 2.322
C. 0 and 0.431
D. 0.431
3. Which of the following is not a property of logarithms?
A.
B.
C.
D.
4. A falling object has velocity 37(1 − e–0.4t) meters per second after t seconds of free fall. Which of the following statements is true?
A. Its initial velocity was 0 meters per second and its velocity after 10 seconds is –12.2 meters per second.
B. Its initial velocity was –1 meter per second and its velocity after 10 seconds is –36.3 meters per second.
C. Its initial velocity was 0 meters per second and its velocity after 10 seconds is 36.3 meters per second.
D. Its initial velocity was 1 meter per second and its velocity after 10 seconds is 12.2 meters per second.
5. How many roots does x6 = 3x5 + 1 have?
A. 6
B. 5
C. 11
D. 1
6. If 2 − i is a root of 3x3 − 11x2 + 11x + 5, then what are its other roots?
A.
B.
C.
D.
7. On which interval does the Intermediate Value Theorem guarantee that the polynomial x4 + 7x2 − 9x − 1 has a root?
A.
B.
C.
D.
8. If 1 and –6 are two of the roots of 6x4 + 31 x3 − 33x2 − 16x + 12, then what are the other two?
A.
B.
C.
D.
9. Which of these graphs could be the graph of y = ex + 1?
A.
B.
C.
D.
10. Why do we use the Intermediate Value and Bisection Theorems to find only the irrational roots of polynomials?
A. It is the only method available for finding irrational roots of any polynomial.
B. The Rational Roots Theorem is better for finding the rational roots.
C. Those theorems are unable to find rational roots.
D. No polynomial has rational roots.
11. A population of 2000 snakes is released into a marshland and grows according to the formula P = 2000 • 1.5t, where t is the number of months after the release. Find the population 10 months after the release.
A. 63,246
B. 115,330
C. 5.9 x 1034
D. 30,000
12. Write in terms of ln a, ln b, and ln c. You may assume that all variables are positive.
A.
B.
C.
D.
13. Which of these is the result of (x5 − x3 + 2x2 − 9x + 5) ÷ (x + 2)?
A.
B.
C.
D.
14. Evaluate .
A. 2
B. 4
C. ¼
D. ½
15. Find the point (x, y) on the parabola y = 9 − x2 such that the shaded rectangle in the figure below has area 20 square units.
A.
B.
C.
D.
16. Solve ln t = log 50 for t.
A. t = 5.47
B. t = 8166.3
C. t = 13.6
D. t = 50
17. Which of the following is the conclusion you can draw using Descartes' Rule of Signs applied to 2x4 − 6x3 + x2 + 7x − 4?
A. Zero is not a root.
There are either 1 or 3 positive real roots.
There are 3 negative real roots.
There are either 0 or 2 complex roots.
B. Zero is not a root.
There are either 1 or 3 positive real roots.
There are 3 negative real roots.
No information is available about the number of complex roots.
C. Zero is not a root.
There are either 1 or 3 positive real roots.
There is 1 negative real root.
There are either 0 or 2 complex roots.
D. Zero is not a root.
There are either 1 or 3 positive real roots.
There is 1 negative real root.
No information is available about the number of complex roots.
18. Which of these is the remainder when 4x4 − 5x3 + 9 is divided by x − 3?
A.
B.
C.
D.
19. Which of these could be the graph of y = 7x − 2?
A.
B.
C.
D.
20. Simplify .
A.
B. 216
C.
D. is already in simplified form.
21. Which of the following is a reason for why the trace function on a graphing calculator can sometimes be better than the Bisection Theorem for finding roots?
A. The trace function always finds an exact root.
B. The Intermediate Bisection Theorem applies only to continuous functions, and not all polynomials are continuous.
C. Some roots aren't surrounded by one positive and one negative value of the polynomial
D. The Bisection Theorem can't find roots to more than 3 decimal places.
22. If a cubic polynomial has roots –5 and 6 − 2i, what is its third root?
A. 1 − 2i
B. –30 + 10i
C. 6 + 2i
D. 5
23. Which of the following is a correct description of the expression logbx?
A. It is the power to which b must be raised to yield x.
B. It is the xth power of b.
C. It is the bth power of x.
D. It is the power to which x must be raised to yield b.
24. Which of the following is equal to log6(t + 1) − log6(t2 − 1)?
A. log6(t + 1)
B. log6t − log6t2
C. log6t
D. –log6(t − 1)
25. Which are upper and lower bounds for the real roots of 3x4 − 2x3 + x − 9 = 0?
A. –3 and –1, 1, and 3
B. –2 and 2
C. –2 and –1, 1, and 2
D. 0 and 3
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 1. Find all roots of x3 + 2x2 + 2x + 1. Hint: Find the rational one(s) first.
Hint: Try the factors of 1.
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No one's gonna do all these problems.
Post them separately, you might get some of them.
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