Find the minimum value of the expression f(x)=A x^2+B x+C whose zeroes are and +2 which can be obtained by the relation =[2 -1] (where 1] denote the greatest integer function) and = _ x 0 1- (1- x) x^4

Step-by-step solution

aligned & = _ x 0 1- 1- (1- x)^2 2! + (1- x)^4 4! + . . x^4 _ x 0 (1- x)^2 2! 1- (1- x)^2 2 3! + . . x^4 & _ x 0 (2 ^2 x 2 )^2 2 x^4 [1- (1- x)^2 2 3! . . ] _ x 0 [1- (1- x)^2 2 3! + . . ] = 1 8 & =[2 -1]= [2 1 8 -1 ]= [- 3 4 ]=-1 aligned Now, =-1, +2=-1+2=1 The quadratic expression is x^2-(-1+1) x+(-1 (-1 1)f(x)=x^2-1 f(x)=2 x-0=0 x=0 Minimum value is (-1)