Let p, q ∈ R. If 2 - √3 is a root of a quadratic equation, x² + px + q = 0, then

Correct option is B. p² - 4q + 12 = 0
In given question p, q ∈ R. If we take other root as any real number α, then quadratic equation will be
x² - (α + 2 - √3)x + α(2 - √3) = 0
Now, we can have none or any of the options can be correct depending upon 'α'.
Instead of p, q ∈ R it should be p, q ∈ Q then other root will be 2 + √3
⇒ p = -(2 + √3 + 2 - √3) = -4
and q = (2 + √3)(2 - √3) = 1
⇒ p² - 4q - 12 = (-4)² - 4(1) - 12 = 16 - 4 - 12 = 0
Option (2) is correct.