Question

Find the real or imaginary solutions of each polynomial equation by factoring.
2x+4x^2-30x

How do I do this?

Answer 1

Also Find the real solutions of the equation by graphing
2x+4x^2-30x

Answer 2

Wait, can you factor a quadratic equation?

Answer 3

I think its what it says in my paper

Answer 4

Okay...but can you factor a quadratic equation?

Answer 5

yep

Answer 6

i just forgot how to do it. Its for review.

Answer 7

Notice that your expression be written as \[4x^{2}-28x\]

Answer 8

Look at the expression and see if there is anything that is common to both of them

Answer 9

They could be divided by 4x

Answer 10

Yes. How can you show that?

Answer 11

4x(x-7)?

Answer 12

Correct. You have factored it.

Answer 13

Ok. Thanks that was really easy, I can't believe I forgot how to do that. Could you help me with the second one?

Answer 14

We haven't found real or imaginary solutions yet.

Answer 15

Oh so theres more to it?

Answer 16

Its says so in the question.

Answer 17

Ok could you help me with that too? Please

Answer 18

The factored expression set to equal to zero and solve for x.

Answer 19

How would I do that? I'm confused.

Answer 20

Would one root be 0 and the other 7?

Answer 21

Yes. Those are the roots, 0 and 7. This equation has no imaginary roots.

Answer 22

How do you know when there are imaginary roots?

Answer 23

If one of the x values is the square root of a negative number.

Answer 24

ok I get it. Now I think I got it. Thanks so much.

Answer 25

Good!!!

Answer 26

Now the second question. Is that easier?

Answer 27

0 and 7 are real numbers, thus they are also real solutions. I don't see the point graphing it again just to see 0 and 7 on the graph.

Answer 28

ok

Answer 29

To graph it you will find, x intercept (which is just the roots we have already found), y intercept, and vertex.

Answer 30

Still wanna?

Answer 31

would it be 0,7?

Answer 32

What?