Respuesta :

VirαtKσhli

Given :-

  • The roots of the function are 5 and -3 .

To Find :-

  • The Quadratic function .

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.