Polynomial Functions Worksheet With Answer Key Page 9
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17Advanced Algebra Honors
Wkst 6-5: Theorems About Roots of Polynomial Equations
39.
A polynomial equation with rational coefficients has the given roots. Find two additional
roots.
1. 2 + 3i and
2. 3 −
2 and 1 +
7
3
3. − 4 i and 6 − i
4. 5 −
6 and − 2 + 10
40.
Find a fourth-degree polynomial equation with integer coefficients that has
the given numbers as roots.
5. 2 i and 4 − i
6.
2 and 2 −
3
7. 3 i and
6
8. 2 + i and 1 −
5
Find the roots of each polynomial equation.
3
2
3
2
9. x
− 5 x
+ 2 x + 8 = 0
10. x
+ x
− 17 x + 15 = 0
3
2
3
2
11. 2 x
12. x
+ 13 x
+ 17 x − 12 = 0
− x
− 34 x − 56 = 0
3
4
2
13. x
− 18 x + 27 = 0
14. x
− 5 x
+ 4 = 0
3
2
3
2
15. x
16. x
− 6 x
+ 13 x − 10 = 0
− 5 x
+ 4 x + 10 = 0
3
2
3
17. x
− 5 x
+ 17 x − 13 = 0
18. x
+ x + 10 = 0
3
2
3
19. x
− 5 x
− x + 5 = 0
20. x
− 12 x + 16 = 0
3
2
3
2
21. x
− 2 x
− 5 x + 6 = 0
22. x
− 8 x
− 200 = 0
3
2
3
2
23. x
+ x
− 5 x + 3 = 0
24. 4 x
− 12 x
− x + 3 = 0
3
2
3
2
25. x
+ x
− 7 x + 2 = 0
26. 12 x
+ 31 x
− 17 x − 6 = 0
Use the Rational Root Theorem to list all possible rational roots for each polynomial
equation. Then find any actual rational roots.
3
2
3
2
27. x
+ 5 x
− 2 x − 15 = 0
28. 36 x
+ 144 x
− x − 4 = 0
3
2
4
3
2
29. 2 x
+ 5 x
+ 4 x + 1 = 0
30. 12 x
+ 14 x
− 5 x
− 14 x − 4 = 0
3
2
3
2
31. 5 x
− 11 x
+ 7 x − 1 = 0
32. x
+ 81 x
− 49 x − 49 = 0
Find a third-degree polynomial equation with rational coefficients that has the given
numbers as roots.
33. 3, 2 − i
34. 5, 2 i
35. − 1, 3 + i
36. − 7, i
37. − 4, 4 i
38. 6, 3 − 2 i
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