For this case we have the following roots:
[tex]x_ {1} = - 3\\x_ {2} = 5[/tex]
We must find a quadratic function associated with the given roots.
We have to, we can represent the solution as follows:
[tex](x + 3) (x-5) = 0\\x_ {1} = - 3\\x_ {2} = 5[/tex]
If we apply distributive property considering that:
[tex]+ * - = -[/tex]
Different signs are subtracted and the major sign is placed.
[tex](x + 3) (x-5) = x ^ 2-5x + 3x-15 = x ^ 2-2x-15[/tex]
Thus, the quadratic function is:
[tex]f (x) = x ^ 2-2x-15[/tex]
Answer:
[tex]f (x) = x ^ 2-2x-15[/tex]
