Explanation

Let's use the quadratic formula to find the roots:

x = (-b ± √(b² - 4ac)) / 2a

For the given equation x² - 3x + k + 1 = 0:

a = 1, b = -3, c = k + 1

The roots differ by unity, so:

√(b² - 4ac) = 1

(-3)² - 4(1)(k + 1) = 1

9 - 4k - 4 = 1

5 - 4k = 1

-4k = -4

k = 1