Question

Use the Zero Product Property to find the values of x that make the equation true.(x−4)(2x+5)=0 Show your work on paper, take a picture, then upload it here!

Answer 1

Recall that:

`ab=0`

if and only if:

`a=0\text{ or b=0.}`

Therefore:

`(x-4)(2x+5)=0,`

if and only if:

`x-4=\text{ or }2x+5=0.`

Solving each equation for x, we get:

`\begin{gathered} x-4+4=0+4, \\ x=4, \\ 2x+5=0, \\ 2x=-5, \\ x=-(5)/(2). \end{gathered}`

Answer:

`x=4,\text{ or }x=-(5)/(2).`