ShmoopTube

00:02

And here's another shmoop du jour.

00:04

Which of the following is the solution set of the equation x squared + 3x - 10 = 0?

00:10

Here are the potential answers…

00:15

We are told that the answers are all either 2 or 5, positive or negative.

00:20

And because of the format of the equation we know it’s a quadratic,

00:24

so we know it can be solved by factoring.

00:27

That is, the answer is going to be of the format “x plus or minus something”…

00:31

with parentheses around it… times the same thing, also plus or minus.

00:36

So start with the x’s here and here with the parentheses around ‘em.

00:40

Now we need a 2 and a 5 on either end – we could have figured that out because we need

00:44

them to multiply out to be 10 and the only factors of 10 are 1 and 10 and 2 and 5…

00:51

…and since the middle term has a 3 in it, it can’t be 1 minus 10 or 10 minus 1.

00:57

So it’s either 2 or 5.

01:00

And we also know that one term has to be positive and one has to be negative because we need

01:06

a NEGATIVE 10 on the end there.

01:08

We need a POSITVE 3… so the 5 has to be positive and the 2 negative.

01:14

Now we’ve got the quantity x minus 2 times the quantity x plus 5.

01:19

And our answer is B.

Full Transcript