# Thread: More to come from me !! It’s been a while

1. ## More to come from me !! It’s been a while

Solve a^2 - 7a - 30 = 0

2. ## Re: More to come from me !! It’s been a while

I would factor here...can you name two factors of -30 whose sum is -7?

3. ## Re: More to come from me !! It’s been a while

Oh I see, it is -10 and 3, but than my question is what is done with the 0 after the GCF is found

4. ## Re: More to come from me !! It’s been a while

Also, what happens to the a in 7a?

5. ## Re: More to come from me !! It’s been a while

Originally Posted by Eddyrodriguez
Oh I see, it is -10 and 3, but than my question is what is done with the 0 after the GCF is found
Yes, and so we may write:

$\displaystyle a^2-7a-30=(a-10)(a+3)=0$

Now, equate each factor to zero, and solve for a to get the two roots.

6. ## Re: More to come from me !! It’s been a while

The basic point in solving problems like this is the "zero product property": "if ab= 0 then either a= 0 or b= 0". Once you have that $\displaystyle (a- 10)(a+ 3)= 0$ then we must have either $\displaystyle a- 10= 0$ or $\displaystyle a+ 3= 0$. That gives, of course, two different values for a either of which satisfies the original equation.