# DESCARTES RULE OF SIGNS PRACTICE PROBLEMS

State the possible number of positive and negative zeros for each function.

Problem 1 :

f(x) = 3x4 + 20x2 - 32

Solution

Problem 2 :

f(x) = 5x4 - 42x2 + 49

Solution

Problem 3 :

f(x) = 4x3 - 12x2 - 5x + 1

Solution

Problem 4 :

f(x) = 2x4 - 3x3 + x

Solution

Problem 5 :

f(x) = 2x4 + 3x2 - 54

Solution

Problem 6 :

f(x) = x6 - 64

Solution

Problem 7 :

f(x) = 9x6 - 3x5 + 33x4 - 11x3 + 18x2 - 6x

Solution

Problem 8 :

f(x) = 64x6 - 1

Solution

Problem 9 :

f(x) = 2x5 + 4x4 + 9x3 + 18x2 - 35x - 70

Solution

Problem 10 :

f(x) = 6x5 - 4x4 - 63x3 + 42x2 + 147x - 98

Solution

Problem 11 :

f(x) = 16x6 - 32x4 - 25x2 + 50

Solution

Problem 12 :

f(x) = x7 - 64x

Solution

1) Number of positive roots = 1, negative rots = 1 and imaginary roots = 2

2)

3)

4)

5) number of positive roots = 1, number of negative roots = 1, number of imaginary roots = 2.

6) number of positive roots = 1, number of negative roots = 1, number of imaginary roots = 4.

7)

8) number of positive roots = 1, number of negative roots = 1, number of imaginary roots = 4.

9)

10)

11)

12) Number of positive roots = 1, negative roots = 1 and imaginary roots = 5.

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