Expert: Richard J. Raridon - 8/20/2009

Question
List the possible rational roots for the equation:

x3 + x2 - 4x + 4 = 0


{±1, ±2, ±4}  No answer is correct.
{1, 2, 4}  {±1, -2}

2. List the possible rational roots for the equation:

x4 + 3x3 - x2 - 9x - 6 = 0


-2, -1, ±Ö 3
 {1, 2, 3, 6}
No answer is correct.  {±1, ± 2, ± 3, ± 6}

3. List the possible rational roots for the equation:  

x4 + 3x2 - 8x + 10 = 0


{±1, 5, 10}  {±1, ± 2, ± 5, ± 10}
{1, 2, 5, 10}  No answer is correct.

4. List the possible rational roots for the equation:

2x3 - 5x2 - 11x - 4 = 0


{-1, -0.5, 4}  No answer is correct.
{±1, ± 2, ± 4, ± 0.5}  {1, 2, 4, 0.5}

5. List the possible rational roots for the equation:

4x4 + 4x3 + 17x2 + 16x + 4 = 0


{±1, ± 4, ± 0.5}  No answer is correct.
{1, 2, 4, 0.5, 0.25}  {±1, ± 2, ± 4, ± 0.5, ± 0.25}

6. List the possible rational roots for the equation:

6x4 - 7x3 + 8x2 - 7x + 2 = 0


{±1, ± 2, ± 1/2, ± 1/3, ± 2/3, ± 1/6}  {±1, ± 1/2, ± 2/3}
{1, 2, 1/2, 1/3, 2/3,1/6}  No answer is correct.

7. List the possible rational roots for the equation:

x4 + 2x + 2 = 0


{-0.5}  No answer is correct.
{±1, ± 2,}  {±1, ± 2, ± 0.5}

8. List the possible rational roots for the equation:

8x3 + 6x2 - 5x + 1 = 0


{-1, - 1/2, - 1/4, - 1/8}  No answer is correct.
{±1, ± 1/2, ± 1/4, ± 1/8}  {1, 1/2, 1/4, 1/8}

9. Assume that y varies directly as x. If y = 4 when x = 0.5, find y when x = 2. y = 4  y = 16
y = 6  y = 8

10. Assume that y varies directly as x. If y = 3.2 when x = 0.2, find y when x = 1.6. y = 2.56  y = 0.01
y = 0.1  y = 25.6

11. Assume that y varies inversely as x. If y = 3.2 when x = 0.2, find y when x = 1.6. y = 4  y = 2.5
y = 0.4  y = 25

12. Assume y varies inversely as x. If y = 24 when x = 3, what is y when x = 8? 2  9
5  8

13. Assume y varies inversely as x. If y = -32 when x = 2, what is x when y = 4? -12  -14
-18  -16

14. A number y varies inversely as the square of x. If y = 2 when x = 6, what is y when x = 3? 6  4
8  10

15. The length of a rectangle with constant area varies inversely as the width. When the length is 18 ft, the width is 8 ft. Find the length when the width is 9 ft. 12 ft  14 ft
16 ft  18 ft

16. The height of a cylinder with constant volume is inversely proportional to the square of its radius. If h = 8 cm when r = 4 cm, what is r when h = 2 cm? 6 cm  12 cm
14 cm  8 cm

17. Find all the roots of the equation.

x3 - 2x2 - x + 2 = 0

No roots  0, -1
-1, 1, 2  -1

18. Find all roots of the equation

x3 - x2 - 14x + 24 = 0

-4, 2, 3  4, 2, 3
0, 4  -4, 3
32. Solve the following equation:

x4 + 2x + 2 = 0


19. Find all roots of the equation

34. Solve the following equation:

2x3 - 5x2 - 11x - 4 = 0

6y5 - 13y4 - 6y3 + 17y2 - 4 = 0

-1, -0.5, 2/3, 1, 2  1, 0.5, 2/3, -1, -2
-1, 0.5, 1, 2  0, -1, -0.5, 2/3, 1, 2

20. Find all the zeros of the polynomial

(x + 1)(x - 4)(x2 - 7)

-1, 4  -1, 4, ±Ö 7

No zeros  0

21. Find all zeros of the polynomial

x3 - 5x2 + x - 5

5, i  -5, -i
0, 1  5, ± i

22. Find all rational roots of:

x5 - 2x4 + 11x3 - 22x2 - 12x + 24 = 0

1, -1  1, -1, 2
0, 1, 2  i, -i, 1, 2

23. Use the Rational Roots Theorem to solve the equation for the rational roots

x3 - 3x2 + 4x - 12 = 0

-3, 0  4, 12, 3
3  3, ± 2i

24. Use the Rational Roots Theorem to solve the equation for the rational roots

x4 - 2x3 - 8x2 + 10x + 15 = 0

No rational roots  i, -2i
-1, 3  1, -3

25. Use the Rational Roots Theorem to solve the equation for the rational roots.

4y5 + 8y4 - 29y3 - 42y2 + 45y + 54 = 0

-3, 2, -1, ± 1.5  -3, 1.5, -1
2, -1.5, -1, 3  8, -2, 3, 1.5

26. Use the Rational Roots Theorem to solve for the rational roots

3x4 - 2x3 + 8x2 - 6x - 3 = 0

-1/3, 1, -i  -1/3, 1
1/3, -1  1, i

27. Use the Rational Roots Theorem to solve for the rational roots

8y4 - 6y3 + 17y2 - 12y + 2 = 0

0.25, 0.5  0.25, 0.5, ± i
-0.25, -0.5, -i  -0.25, -0.5

28. Find all the roots of the equation:

P(x) = 0.25x2 - 12x + 23

2, 46  2, 11
3, 4/5  -1, 7

29. Find all roots of the equation

3x2 - 11x - 4 = 0

-3, 4  3, 4
-1/3, 4  4

30. List the possible rational roots of the following equation:

5x4 + 9x3 + 5x2 + 2x + 4 = 0

31. List the possible rational roots of the following equation:

3x4 + 5x3 + 3x2 - 7x + 9 = 0

33. Solve the following equation:

x4 + 3x3 - x2 - 9x - 6 = 0


Answer
1. no answer is correct
2. -1, -2, +/- 3^1/2
3. no answer
4. -1, -0.5, 4
5. no answer
6. no answer
7. no answer
8. no answer
9. y=16
10. y = 25.6
11. y = 0.4
12. y = 9
13. -16
14. 8
15. 16
16. r = 8
17. 1, -1, 2
18. 2, 3, -4
32. no real solution
19. 2x^3-5x^2-11x-4 = 0, x = -1/2, -1, 4
34. y = -1
20. -1, 4, +/- 7^1/2
21. 5, +/- i
22. +/- 1
23. 3, +/- 2i
24. -1, 3
after two hours I got tired