4.

The roots of the equation x2 + 16 = 4bx are real if :

b 2

Step-by-step explanation:

Given

x² + 16 = 4bx (subtract 4bx from both sides)

x² - 4bx + 16 = 0 ← in standard form

with a = 1, b = - 4b, c = 16

For the roots to be real the discriminant b² - 4ac > 0, that is

( - 4b) ² - (4 * 1 * 16) > 0

16b² - 64 > 0

16 (b² - 4) > 0 ← factor using difference of squares

16 (b - 2) (b + 2) > 0, thus

b 2