Gabby solve {x^2} - x - 20 = 0 as shown below: \begin{array}{l}{x^2} - x - 20 = 0\\\left( {x - 5} \right)\left( {x + 4} \right) = 0\\x = - 5,4\end{array} Caitlyn says Gabby is wrong and believe this is the solution: \begin{array}{l}{x^2} - x - 20 = 0\\\left( {x - 5} \right)\left( {x + 4} \right) = 0\\x = 5, - 4\end{array} Is Gabby or Caitlyn correct? Explain the error made by the incorrect girl.

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Gabby solve {x^2} - x - 20 = 0 as shown below: \begin{array}{l}{x^2} - x - 20 = 0\\\left( {x - 5} \right)\left( {x + 4} \right) = 0\\x = - 5,4\end{array} Caitlyn says Gabby is wrong and believe this is the solution: \begin{array}{l}{x^2} - x - 20 = 0\\\left( {x - 5} \right)\left( {x + 4} \right) = 0\\x = 5, - 4\end{array} Is Gabby or Caitlyn correct? Explain the error made by the incorrect girl.

Mathematics
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Well, first we have to know that when we say `a•b=0` (in general) THEN, either a or b has to be equal to 0. is this information correct?
by correct you mean the way it was typed ?
I mean that the point I made (as regards to the math part)

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that the point I made is correct or not
{x^2} - x - 20 = 0 this is the problem they are working out
yes, yes, I know.... I am asking you if you are {familiar with/ understand the} the zero product property
not really
You know if you say `x • y = 0` then for it to be true, either x=0, or y=0
Right?
yes
Ok, now back to our problem....
he factored the quadratic equation, and now he has: \(\large\color{black}{ \displaystyle (x-5)(x+4)=0 }\)
Then, this "zero product property" (as I showed with `y•x=0`) has to work here too.
That means that either x-5 =0 or that x+4 =0 Correct or not?
Now, for what value of x is x-5=0? And for what value of x is x+4=0?
it would be 4, and 5 ?
Please in order, and please try again
it would be -5, 4
x-5=0 x+4=0 (-5)-5=0 (4)+4=0 according to what you said:
so the property that they did wrong was the zero property
who did wrong?
Caitlyn and Gabby
One of them is correct. (But only one is correct, the other is wrong)
|dw:1437049882899:dw|
so would Gabby be correcr ?
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so it would be Catilyn who is right ?
|dw:1437050054286:dw|
it seems as though you are trying to guess the answer....
x= -4 and x=5
yes
x=-4, x=5 that is correct

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