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