Question

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.

Answer 1

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?

Answer 2

by correct you mean the way it was typed ?

Answer 3

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

Answer 4

that the point I made is correct or not

Answer 5

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

Answer 6

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

Answer 7

not really

Answer 8

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

Answer 9

Right?

Answer 10

yes

Answer 11

Ok, now back to our problem....

Answer 12

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

Answer 13

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

Answer 14

That means that either x-5 =0
or that x+4 =0

Correct or not?

Answer 15

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

Answer 16

it would be 4, and 5 ?

Answer 17

Please in order, and please try again

Answer 18

it would be -5, 4

Answer 19

x-5=0 x+4=0
(-5)-5=0 (4)+4=0

according to what you said:

Answer 20

so the property that they did wrong was the zero property

Answer 21

who did wrong?

Answer 22

Caitlyn and Gabby

Answer 23

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