Given the quadratic equations I. 9a² + 18a + 5 = 0 and II. 2b² + 13b + 20 = 0, determine the correct relationship between the values of a and b after solving both equations.

Explanation

Solving equation I: 9a² + 18a + 5 = 0 can be factored as (3a + 5)(3a + 1) = 0, giving roots a = -5/3 and a = -1/3. Solving equation II: 2b² + 13b + 20 = 0 factors as (2b + 5)(b + 4) = 0, giving roots b = -5/2 and b = -4. Comparing the roots, each value of a is greater than each value of b, hence a > b.