Let α₁, ₂ and B₁, B₂ be the roots of ax² + bx + c = 0 and px² + qx + r = 0, respectively. If the system of equations a₁ + a₂z = 0 and B₁y+ B₂z = 0 has a non-trivial solution, then prove that b²pr=q²ac.

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