If a and b are the roots of the quadratic equation x² + 8x + 4 = 0, what is the value of a/b plus b/a?

Explanation

To find a/b + b/a, rewrite it as (a² + b²) / (ab). Using the identity (a + b)² = a² + 2ab + b², we get a² + b² = (a + b)² - 2ab. From the quadratic, the sum of roots a + b = -8 and the product ab = 4. Substituting these values, a/b + b/a = [(−8)² − 2 × 4] / 4 = (64 − 8) / 4 = 56 / 4 = 14.