Problem 5.1: How many variations are in the function f (x) = x⁶ -6x⁴ +2x² + 2x - 7? [Solution]

Problem 5.2: How many positive and negative real roots might the function f (x) = 2x³ -3x² - 4x + 1 have? [Solution]

Problem 5.3: What are the possible rational roots of f (x) = x³ -4x² + 3x - 6? Use Descartes' Rule of Signs and the Rational Root Theorem. [Solution]

Problem 5.4: Find all real roots of x³ +

x² - 4x - 2. [Solution]

Problem 5.5: Find all real roots of x⁴ +5x³ - 15x + 9. [Solution]