Question

If [(4a², 4a,1),(4b², 4b, 1),(4c², 4c, 1)],[(f(-1)),(f(1)),(f(2))] = [(3a² + 3a),(3b² + 3b),(3c² + 3c)], f(x) is a quadratic function and its maximum value occurs at a point V. A is a point of intersection of y = f (x) with x-axis and point .B is such that chord AB subtends a right angled at V. Find the area enclosed by f(x) and chord AB.

Answer 1

Given,

where f(x) is quadratic expression given by,

f(x)= ax² + bc + c and (i), (ii) and (iii)

Equation of chord AB is