Explanation
We are asked to determine the quadratic equation that has -2 and 3 as its roots
To do so, we will make use of the fact that
if -2 is one of its roots, then
[tex]\begin{gathered} x=-2 \\ (x+2)\text{ is a factor} \end{gathered}[/tex]
Also
[tex]\begin{gathered} x=3 \\ (x-3)\text{ is a factor} \end{gathered}[/tex]
Thus
we have
[tex](x+2)(x-3)=x^2-3x+2x-6=x^2-x-6[/tex]
Therefore, the answer is
