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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.

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  1. SolomonZelman
    • one year ago
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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?

  2. anonymous
    • one year ago
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    by correct you mean the way it was typed ?

  3. SolomonZelman
    • one year ago
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    I mean that the point I made (as regards to the math part)

  4. SolomonZelman
    • one year ago
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    that the point I made is correct or not

  5. anonymous
    • one year ago
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    {x^2} - x - 20 = 0 this is the problem they are working out

  6. SolomonZelman
    • one year ago
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    yes, yes, I know.... I am asking you if you are {familiar with/ understand the} the zero product property

  7. anonymous
    • one year ago
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    not really

  8. SolomonZelman
    • one year ago
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    You know if you say `x • y = 0` then for it to be true, either x=0, or y=0

  9. SolomonZelman
    • one year ago
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    Right?

  10. anonymous
    • one year ago
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    yes

  11. SolomonZelman
    • one year ago
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    Ok, now back to our problem....

  12. SolomonZelman
    • one year ago
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    he factored the quadratic equation, and now he has: \(\large\color{black}{ \displaystyle (x-5)(x+4)=0 }\)

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

  14. SolomonZelman
    • one year ago
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    That means that either x-5 =0 or that x+4 =0 Correct or not?

  15. SolomonZelman
    • one year ago
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    Now, for what value of x is x-5=0? And for what value of x is x+4=0?

  16. anonymous
    • one year ago
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    it would be 4, and 5 ?

  17. SolomonZelman
    • one year ago
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    Please in order, and please try again

  18. anonymous
    • one year ago
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    it would be -5, 4

  19. SolomonZelman
    • one year ago
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    x-5=0 x+4=0 (-5)-5=0 (4)+4=0 according to what you said:

  20. anonymous
    • one year ago
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    so the property that they did wrong was the zero property

  21. SolomonZelman
    • one year ago
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    who did wrong?

  22. anonymous
    • one year ago
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    Caitlyn and Gabby

  23. SolomonZelman
    • one year ago
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    One of them is correct. (But only one is correct, the other is wrong)

  24. triciaal
    • one year ago
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    |dw:1437049882899:dw|

  25. anonymous
    • one year ago
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    so would Gabby be correcr ?

  26. triciaal
    • one year ago
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    |dw:1437050014096:dw|

  27. anonymous
    • one year ago
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    so it would be Catilyn who is right ?

  28. SolomonZelman
    • one year ago
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    |dw:1437050054286:dw|

  29. SolomonZelman
    • one year ago
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    it seems as though you are trying to guess the answer....

  30. anonymous
    • one year ago
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    x= -4 and x=5

  31. SolomonZelman
    • one year ago
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    yes

  32. SolomonZelman
    • one year ago
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    x=-4, x=5 that is correct

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