Question

Can someone show me how to use the Zero Product Property to find the root of: x^2+6x ?

Answer 1

do you mean x^2+6x = 0 ?

Answer 2

Yeah.

Answer 3

factor out an x from those terms

x^2+6x = 0
x( .... ) =0

Answer 4

can you do this?

Answer 5

I'm a little confused...

Answer 6

you know how x^2 is the same as x*x right?

Answer 7

Yes.

Answer 8

so you have

x^2+6x = 0
x*x+6*x = 0

on the left hand side both terms have a factor of x

factor it out

like this (ab+cb) = b(a+c)

Answer 9

x*x+6*x = x( .... + ...)

Answer 10

I think I'm just confused because there is no value in the middle. Before this question I answered: \[3x ^{2}-7x+4=(x-1)(3x-4)\] I used a generic rectangle to factor it out, and I'm only comfortable doing these with a value like the 4.

Answer 11

that is factoring a quadratic,

this question in not a quadratic, its easier

Answer 12

Ohhh! Okay, but I'm still confused, could you dumb it up a little bit more?

Answer 13

you know how to expand brackets like this right?

2(y+3) = 2y+6

the factoring step is the reverse

2y+6 = 2(y+3)

Answer 14

xx+6x = x( ...+ ...)

Answer 15

what are the dots?

Answer 16

x+6?

Answer 17

yes

x^2+6x = 0
x(x+6) =0

Answer 18

now you have two terms, and their product equals zero

for this to be true, one of the factors either x or (x+6) must equal zero

Answer 19

so x=0 or x+6=0

what values for x satisfy this ?

Answer 20

Well, 0 for the first one, and -6 for the second?

Answer 21

Correct!

Answer 22

so those are the two roots.

Answer 23

if you were to graph the equation

you would get something like this

Answer 24

Thank you so much! @UnkleRhaukus