Let f(x) = x⁴ + ax³ + bx² + c be a polynomial with real coefficients such that f(1) = −9. Suppose that i√3 is a root of the equation 4x³ + 3ax² + 2bx = 0, where i = √−1. If α₁, α₂, α₃, and α₄ are all the roots of the equation f(x) = 0, then |α₁|² + |α₂|² + |α₃|² + |α₄|² is equal to ________.