Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

The function $f(x) = {x^3} - 6{x^2} + ax + b$ is such that $f(2) = f(4) = 0$. Consider two statements : Statement 1 : there exists x₁, x₂ $\in$(2, 4), x₁ < x₂, such that f'(x₁) = $-$1 and f'(x₂) = 0. Statement 2 : there exists x₃, x₄ $\in$ (2, 4), x₃ < x₄, such that f is decreasing in (2, x₄), increasing in (x₄, 4) and $2f'({x_3}) = \sqrt 3 f({x_4})$. Then