Given :-
To Find :-
Answer :-
The roots of the function are 5 and -3 . In general we can write the Quadratic function with roots π and ∆ as ,
[tex]\sf\longrightarrow[/tex] f(x) = ( x - π )(x-∆)
So on using this we have ,
[tex]\sf\longrightarrow[/tex] f(x) = ( x -5)( x -(-3))
[tex]\sf\longrightarrow[/tex] f(x) = (x-5)(x+3)
[tex]\sf\longrightarrow[/tex] f(x) = x(x-5)+3(x-5)
[tex]\sf\longrightarrow[/tex] f(x) = x² -5x +3x -15
[tex]\sf\longrightarrow[/tex] f(x) = x² -2x -15
Hence the required answer is x² -2x -15.