How do you do y^2+3y+2=0?

Question

How do you do y^2+3y+2=0?

I know how to factor it, but now that it has a =0 after it, i am a little confused of what to do with it.

Any help will be greatly appreciated!

Thank you!

Answer 1

So, once you factor the left side of this equation it works out to be: (y+2)(y+1)=0

Now what do you do with this =0 part?
The Zero Product property states that when you multiply anything by 0, the answer will be zero.
So if you have an equation like a*b=0, you know that either a=0 or b=0, or both, in order to result in 0.
The factored version of your equation is in this same format.

In order to solve for y, you must set each factor equal to zero.
y+2=0    and     y+1=0
Then you subtract each to find that y=-2 and y=-1

You can take these two answers and check them by plugging them back into the original equation
(-2)^2+3(-2)+2=0
              4-6+2=0
                     0=0

(-1)^2+3(-1)+2=0
              1-3+2=0
                     0=0

I hope this helps!

Answer 2

If you know how to factor it, you're more than half way there.

y² + 3y + 2 can be factored as (y+2)(y+1) so the equation becomes:

(y+2)(y+1) = 0

Now you have a product of two real numbers equal to zero. This happens if and only if one of the factors is zero, that is:

(y+2) =  0 or (y+1) = 0

And then you have two solutions: x = -2 and x = -1.

Hope this helps!