Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Without using a calculator, find all the roots of each equation.

8. x 3 − 3 x 2 + x − 3 = 0 x cubed , minus , 3 x squared , plus x minus 3 equals 0
9. x 3 + x 2 + 4 x + 4 = 0 x cubed , plus , x squared , plus 4 x plus 4 equals 0
10. x 3 + 4 x 2 + x − 6 = 0 x cubed , plus 4 , x squared , plus x minus 6 equals 0
11. x 3 − 5 x 2 + 2 x + 8 = 0 x cubed , minus , 5 x squared , plus 2 x plus 8 equals 0
12. x 4 + 4 x 3 + 7 x 2 + 16 x + 12 = 0 x to the fourth , plus 4 , x cubed , plus , 7 x squared , plus 16 x plus 12 equals 0
13. x 4 − 4 x 3 + x 2 + 12 x − 12 = 0 x to the fourth , minus , 4 x cubed , plus , x squared , plus 12 x minus 12 equals 0
14. x 5 + 3 x 3 − 4 x = 0 x to the fifth , plus 3 , x cubed , minus 4 x equals 0
15. x 5 − 8 x 3 − 9 x = 0 x to the fifth , minus , 8 x cubed , minus 9 x equals 0

See Problem 2.

Find all the zeros of each function.

16. y = 2 x 3 + x 2 + 1 y equals , 2 x cubed , plus , x squared , plus 1
17. f ( x ) = x 3 − 3 x 2 + x − 3 f open x close equals . x cubed , minus , 3 x squared , plus x minus 3
18. g ( x ) = x 3 − 5 x 2 + 5 x − 4 g open x close equals . x cubed , minus , 5 x squared , plus 5 x minus 4
19. y = x 3 − 2 x 2 − 3 x + 6 y equals , x cubed , minus , 2 x squared , minus 3 x plus 6
20. y = x 4 − 6 x 2 + 8 y equals , x to the fourth , minus , 6 x squared , plus 8
21. f ( x ) = x 4 − 3 x 2 − 4 f open x close equals . x to the fourth , minus , 3 x squared , minus 4
22. y = x 3 − 3 x 2 − 9 x y equals , x cubed , minus , 3 x squared , minus 9 x
23. y = x 3 + 6 x 2 + x + 6 y equals , x cubed , plus 6 , x squared , plus x plus 6
24. y = x 4 + 3 x 3 + x 2 − 12 x − 20 y equals , x to the fourth , plus 3 , x cubed , plus , x squared , minus 12 x minus 20
25. y = x 4 + x 3 − 15 x 2 − 16 x − 16 y equals , x to the fourth , plus , x cubed , minus , 15 x squared , minus 16 x minus 16

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