Two chemical models describe the rate of reaction RRR as a function of temperature TTT. The models are defined by the quadratic expressions R1(T)=4T2+αT+βR_1(T) = 4T^2 + \alpha T + \betaR1(T)=4T2+αT+β and R2(T)=4T2+γT+δR_2(T) = 4T^2 + \gamma T + \deltaR2(T)=4T2+γT+δ. Both models are found to share a common linear factor of (2T−7)(2T - 7)(2T−7).
Show that 7(γ−α)=2(β−δ)7(\gamma - \alpha) = 2(\beta - \delta)7(γ−α)=2(β−δ).
Fully justify your answer.
