anonymous one year ago 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.

1. SolomonZelman

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?

2. anonymous

by correct you mean the way it was typed ?

3. SolomonZelman

I mean that the point I made (as regards to the math part)

4. SolomonZelman

that the point I made is correct or not

5. anonymous

{x^2} - x - 20 = 0 this is the problem they are working out

6. SolomonZelman

yes, yes, I know.... I am asking you if you are {familiar with/ understand the} the zero product property

7. anonymous

not really

8. SolomonZelman

You know if you say x • y = 0 then for it to be true, either x=0, or y=0

9. SolomonZelman

Right?

10. anonymous

yes

11. SolomonZelman

Ok, now back to our problem....

12. SolomonZelman

he factored the quadratic equation, and now he has: $$\large\color{black}{ \displaystyle (x-5)(x+4)=0 }$$

13. SolomonZelman

Then, this "zero product property" (as I showed with y•x=0) has to work here too.

14. SolomonZelman

That means that either x-5 =0 or that x+4 =0 Correct or not?

15. SolomonZelman

Now, for what value of x is x-5=0? And for what value of x is x+4=0?

16. anonymous

it would be 4, and 5 ?

17. SolomonZelman

18. anonymous

it would be -5, 4

19. SolomonZelman

x-5=0 x+4=0 (-5)-5=0 (4)+4=0 according to what you said:

20. anonymous

so the property that they did wrong was the zero property

21. SolomonZelman

who did wrong?

22. anonymous

Caitlyn and Gabby

23. SolomonZelman

One of them is correct. (But only one is correct, the other is wrong)

24. triciaal

|dw:1437049882899:dw|

25. anonymous

so would Gabby be correcr ?

26. triciaal

|dw:1437050014096:dw|

27. anonymous

so it would be Catilyn who is right ?

28. SolomonZelman

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29. SolomonZelman

it seems as though you are trying to guess the answer....

30. anonymous

x= -4 and x=5

31. SolomonZelman

yes

32. SolomonZelman

x=-4, x=5 that is correct