Given the equations (i) a² - 9a + 20 = 0 and (ii) 2b² - 5b - 12 = 0, determine the correct relationship between the values of a and b.

Explanation

Solving equation (i), we factorize as (a - 5)(a - 4) = 0, giving a = 5 or 4. For equation (ii), factorizing 2b² - 5b - 12 = 0 results in (2b + 3)(b - 4) = 0, so b = -3/2 or 4. Comparing the roots, the smallest value of a is 4 and the smallest value of b is -3/2, while the largest values for both are 5 and 4 respectively. Therefore, in all cases, a is greater than or equal to b.