How the Zero Product Property is Used?

[jesi5]

Hey everyone I have been tryin to figure out htis problem for a while can someone show me how to figure it out..{{not just give me the answer}}

Find all solutions to the following equations. Then Explain how the zero Product Property is used.

42.) x^2-x-20=0 43.) 2x^2+7x=15

 

[arthur ohlsten]

42)
x^2-x-20=0 factor
factors of 1 1,1
factors of 20 1,20 2,10 4,5
we want a set whose difference of products = -1
1,1 and 5,4 does it
[x-5][x+4]=0 one or both of the bracketed terms must=0
x-5=0 or x+4=0
x=6 or x=-4 Answer

43)
2x^2+7x=15 rewrite
2x^2+7x-15=0 factor

factors of 2 1,2
factors of 15 1,15 3,5

we want a set whose difference of products =-7
1,2 3,5 does it

[x+5][2x-3]=0 one or both bracketed terms must =0
x=-5 or 2x=3
x=-5 or x=3/2 answer

Arthur

 

[soroban]

Hello, jesi5!

Do you know the "Zero Product Property"?

If the product of two (or more) factors is zero: \(\displaystyle \,a\cdot b\:=\:0\)
. . then at least one of the factors is zero: \(\displaystyle \,a\,=\,0\) or \(\displaystyle b\,=\,0.\)

Find all solutions to the following equations.
Then explain how the Zero Product Property is used.

\(\displaystyle 42)\;x^2\,-\,x\,-\,20\:=\:0\)

Factor: \(\displaystyle \x\,-\,5)(x\,+\,4)\:=\:0\)

We have two quantities whose product is zero.
. . Hence, one of them must be zero.

Hence, either \(\displaystyle x\,-\,5\:=\:0\,\) or \(\displaystyle \,x\,+\,4\:=\:0\)

Then solve the two equations: \(\displaystyle \,\begin{array}{cc}x\,-\,5\:=\:0 & \;\Rightarrow\; & x\,=\,5 \\ x\,+\,4\:=\:0 & \;\Rightarrow\; & x\,=\,-4\end{array}\)