Respuesta :
The roots of the quadratic function are given as,
[tex]\begin{gathered} x\text{ = 8} \\ x\text{ = -5} \end{gathered}[/tex]Sum of roots is calculated as,
[tex]\begin{gathered} sum\text{ of roots = 8 + \lparen-5\rparen} \\ sum\text{ of roots = 8 - 5} \\ sum\text{ of roots = 3} \\ \end{gathered}[/tex]The product of roots is calculated as,
[tex]\begin{gathered} Product\text{ of roots = 8 }\times\text{ \lparen-5\rparen} \\ Product\text{ of roots = -40} \end{gathered}[/tex]The required quadratic function is given as,
[tex]\begin{gathered} x^2-(sum\text{ of roots\rparen x +product of roots = 0} \\ \end{gathered}[/tex]A required quadratic function is calculated as,
[tex]x^2-\text{ 3x-40 = 0}[/tex]Thus the required quadratic function is,
[tex]x^2-\text{ 3x - 40 = 0 }[/tex]