Question

Which of the following is a quadratic equation that has the roots x = 2 and x = −7?

x2 − 5x − 14 = 0
x2 − 5x = −14
x2 + 5x = 14
x2 + 5x = −14

Answer 1

I believe that this is C but would like some clarification. and yeah lunch seems great right now lol @Majesty69

Answer 2

@Maddy1251

Answer 3

i accidentally pressed the wrong name lol

Answer 4

Lol it happens! Do you know how to find roots?

Answer 5

mmm based off of context clues I could figure it out but not off the top of my head, no.

Answer 6

Roots are what makes a function equal 0, when we plug in certain 'x' terms, we get the equation to equal zero. Factoring is a great way to help, however in this case if you do not want to factor, you can plug in your given roots to find what yields 0.

Answer 7

oh also i dont believe its c i think B my bad. I just realized theers a negative but you can still explain. I want to know for sure.

Answer 8

I like all my equations to be set to zero when finding roots.

Answer 9

x2 − 5x − 14 = 0 Good.
x2 − 5x = −14 --> x^2-5x+14=0
x2 + 5x = 14 --> x^2+5x-14=0
x2 + 5x = −14 ----> x^2+5x+14=0.

Answer 10

So, now we can just plug in x=2 and x=-7.

Answer 11

wow really ... I was considering that but im not sure if the zero plays a role, and if i does play a role i dont know how it does.

Answer 12

I will explain why we have zeros first, then proceed.

Answer 13

When we factor an equation like (x+7)(x-5)=0, we want to know how to get (0)(0)=0
In this case x=-7 for the first part, and x=5 for the second. These are known as the roots.

Answer 14

That's just an example, not sure if those roots truly work, but its a vision to see what roots really are and how they work.

Answer 15

Then when you would expand the problem, both of those roots would produce the polynomial to equal zero.

Answer 16

I have to eat real quick, but the answer is C. Try figuring it out to see why it is C.

Answer 17

a hah so far i understand. and ok will do.

Answer 18

I am back.

Answer 19

wow So i was right in the first place when I said C but then I second guess myself because of the negative. However I dont wish to guess that, think you can perhaps explain what happened to the negative.

Answer 20

does it have soemthing to do with cancelling out the numbers?

Answer 21

when I distribute?

Answer 22

No, and well you don't have to distribute. Not yet.

Answer 23

Remember how I set them to zero?

Answer 24

yeah

Answer 25

We have roots x=2 and x=-7

Answer 26

(x+2)(x-7)= ? Distribute that

Answer 27

ok give me a minute

Answer 28

x2 − 5x − 14 = 0 Good.
x2 − 5x = −14 --> x^2-5x+14=0
x2 + 5x = 14 --> x^2+5x-14=0
x2 + 5x = −14 ----> x^2+5x+14=0.
See which of these equals (x+2)(x-7)
Take your time

Answer 29

the two x's make x^2 + x7 - 2x + 14? or was it a minus 14?

Answer 30

0.o a 5? where did that come from?

Answer 31

I will distribute for you.