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.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.