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