Question

now find:
find the zeros:
0 = -5(x + 4)(x - 2)

Explanation:

Step1: Analyze the equation structure

We have the equation \(0 = -5(x + 4)(x - 2)\). Since the product of factors is zero, we can use the zero - product property, which states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both). Here, the factors are \(- 5\), \((x + 4)\) and \((x - 2)\). But \(-5
eq0\) for all real numbers \(x\), so we focus on the other two factors.

Step2: Set each factor to zero

For the factor \((x + 4)\):

Set \(x+4 = 0\). Solving for \(x\), we subtract 4 from both sides of the equation: \(x=-4\).

For the factor \((x - 2)\):

Set \(x - 2=0\). Solving for \(x\), we add 2 to both sides of the equation: \(x = 2\).

Answer:

The zeros of the equation \(0=-5(x + 4)(x - 2)\) are \(x=-4\) and \(x = 2\).