Consider a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. The equation has two distinct real roots, x₁ and x₂. If the sum of the squares of the roots is equal to the square of their sum, i.e., x₁^2 + x₂^2 = (x₁ + x₂)^2, prove that the constant term c is equal to zero.