Problem B4

Let f(z) = az⁴ + bz³ + cz² + dz + e = a(z – r₁)(z – r₂)(z – r₃)(z – r₄) where a, b, c, d, e are integers, a ¹ 0. Show that if r₁ + r₂ is a rational number, and if r₁ + r₂ ¹ r₃ + r₄, then r₁r₂ is a rational number.