Answer:
The two roots of this equation are [tex](-5)[/tex] and [tex]9[/tex].
Step-by-step explanation:
In this question, the goal is to find the values of [tex]x[/tex] that would satisfy this equation- in other words, the value of [tex]x[/tex] should set expression on the left side of the equation [tex](x - 9)\, (x + 5)[/tex] to [tex]0[/tex].
Observe that the expression [tex](x - 9)\, (x + 5)[/tex] is the product of two linear terms, [tex](x - 9)[/tex], and [tex](x + 5)[/tex]. The product of the two is [tex]0[/tex] as long as either of the two terms is [tex]0[/tex]. Hence, the values of [tex]x[/tex] that would satisfy the overall equation [tex](x - 9)\, (x + 5) = 0[/tex] would be the collection of values that would sete either of these terms to [tex]0[/tex].
For example, if [tex](x - 9)[/tex] is to be set to [tex]0[/tex]:
[tex]x - 9 = 0[/tex].
[tex]x = 9[/tex].
Likewise, if [tex](x + 5)[/tex] is to be set to [tex]0[/tex]:
[tex]x + 5 = 0[/tex].
[tex](x + 5) - 5 = 0 -5[/tex].
[tex]x = (-5)[/tex].
In other words, the values of [tex]x[/tex] that would satisfy this equation are [tex](-5)[/tex] and [tex]9[/tex].
