Question

Please help with a zero product property problem?

Answer 1

In the problem, this equation represents the length and width of the base of a box:
x^2 + 60x - 7,200 = 0

I factored and found the solutions to this problem, which are 60 and -120.
These are both working solutions, so they are supposed to represent the length and width of the base of the box, but a box cannot measure a negative number of inches. How do I make it so that the answer works for the situation?

Answer 2

@Loser66

Answer 3

Did you come up with this equation or was it given to you in the problem?

x^2 + 60x - 7,200 = 0

The negative root may well be extraneous but I would like to know the length and width of the base of the box.

Answer 4

This was given to me in the problem.

Answer 5

I checked both solutions, and I found that both of them are working solutions.

Answer 6

So, how do you long the length and width of the box's base?

I understand that you have two correct answers and that one of them is extraneous.

How did you get the two solutions? Did you factor? If so, I think we have the expressions for the length and the width.

Answer 7

Because you have a negative x does not necessarily mean that a side of the box base is negative.

The length of the box base may be 100 - x which for x = -120 is not a negative number.

Answer 8

Yes, I did factor. But when I checked, the answer didn't come out to be extraneous. Where did I go wrong in my calculation?

-120^2 + 60 * (-120) - 7,200 = 0
14,400 + 60 * (-120) - 7,200 = 0
14,400 + (-7,200) - 7,200 = 0
7,200 - 7,200 = 0
0 = 0

Answer 9

For factoring, I got (x - 60) * (x + 120) = 0

It would be great if you could post the original problem as it appear in your text.

It appears that x = 60 is the root that is not extraneous.

60 and 180 may well be the dimensions of the base of the box but I would like to see the original question.

Answer 10

Ok, here is is. The complete question is in the attachment. You can't see my full answer there, so here's that too:

b. (x - 60) = 0
x - 60 = 0
x - 60 + 60 = 0 + 60
x = 60
OR
(x + 120) = 0
x + 120 = 0
x + 120 - 120 = 0 - 120
x = -120

Answer 11

Your A and B are good.

Note that the base is square which needs to be considered.

Answer 12

Oh, yeah, I forgot about that. In that case, the 60 should be the measurement of the length and width, which means the length and width is 60 x 60. Right?

Answer 13

Interesting that the height is given but not the volume of the box.

The base dimensions are x by x so x has to be the positve root.

Answer 14

Yes, the base dimensions have to be 60 by 60.

The -120 is a correct answer to the algebra equation but is not applicable to this box scenario because x has to be positive.

Answer 15

OK, now I understand how this works. Thanks!:)

Answer 16

You are welcome.