Only Parts C D and E please!!!

Consider the following recursively defined function: CO aT(n - 1) +bT(n -2) n2 2 Where a, b area real numbers f(n) satisfies (* if f(n)af(n-1)bf(n-2) is a true statement for n 2. a) For all functions f,g N - R, for any two real numbers a, B, if fin) and gn) satisfy(")for n- 2 then also h(n)-af(n) Bg(n) satisfies it forn2. b)Let 0 be a real number. Show that if fin) q satisfies() for n2 then qis a root of quadratic equation x2-ax-b = 0 c) State and prove the converse of (i). Use this statement and part () to show that if qi, q2 are the roots of 2- ax-b - 0 then h(n)-Aqi B42 satisfies (') for any two numbers A, B d) Consider h(n) from part c). What addistional condition should we impose on the roots ql, q2 so h(n) serves as a closed-form solution for T(n) with A, B uniquely determined? e) Use the previous parts of this question to solve the following recurrence in closed form T(n) 17 5T(n -1) - 6T(n -2) n 2 Consider the following recursively defined function: CO aT(n - 1) +bT(n -2) n2 2 Where a, b area real numbers f(n) satisfies (* if f(n)af(n-1)bf(n-2) is a true statement for n 2. a) For all functions f,g N - R, for any two real numbers a, B, if fin) and gn) satisfy(")for n- 2 then also h(n)-af(n) Bg(n) satisfies it forn2. b)Let 0 be a real number. Show that if fin) q satisfies() for n2 then qis a root of quadratic equation x2-ax-b = 0 c) State and prove the converse of (i). Use this statement and part () to show that if qi, q2 are the roots of 2- ax-b - 0 then h(n)-Aqi B42 satisfies (') for any two numbers A, B d) Consider h(n) from part c). What addistional condition should we impose on the roots ql, q2 so h(n) serves as a closed-form solution for T(n) with A, B uniquely determined? e) Use the previous parts of this question to solve the following recurrence in closed form T(n) 17 5T(n -1) - 6T(n -2) n 2