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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!

Use the Zero Product Property to find the values of x that make the equation true-example-1
User Matthid
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1 Answer

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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).

User Mnickey
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