Question

Write a quadratic function in standard form that has the roots of X=8 and X=-5

Answer 1

The roots of the quadratic function are given as,

$\begin{gathered} x\text{ = 8} \\ x\text{ = -5} \end{gathered}$

Sum of roots is calculated as,

$\begin{gathered} sum\text{ of roots = 8 + \lparen-5\rparen} \\ sum\text{ of roots = 8 - 5} \\ sum\text{ of roots = 3} \\ \end{gathered}$

The product of roots is calculated as,

$\begin{gathered} Product\text{ of roots = 8 }\times\text{ \lparen-5\rparen} \\ Product\text{ of roots = -40} \end{gathered}$

The required quadratic function is given as,

$\begin{gathered} x^2-(sum\text{ of roots\rparen x +product of roots = 0} \\ \end{gathered}$

A required quadratic function is calculated as,

$x^2-\text{ 3x-40 = 0}$

Thus the required quadratic function is,

$x^2-\text{ 3x - 40 = 0 }$