# This equation has two roots

• Oct 15th 2012, 07:55 AM
RD33
This equation has two roots
3x^(6)e^(-2x)-9x^(7)e^(-2x)=0 has two roots

Where do I even start?
• Oct 15th 2012, 08:03 AM
HallsofIvy
Re: This equation has two roots
I would start by dividing through by any non-zero numbers that are common to both sides of the equation. (I presume you know that $e^x$ is not 0 for ny x.)
• Oct 15th 2012, 08:13 AM
Plato
Re: This equation has two roots
Quote:

Originally Posted by RD33
3x^(6)e^(-2x)-9x^(7)e^(-2x)=0 has two roots
Where do I even start?

Factor it: $3x^6e^{-2x}(1-3x)=0~.$
• Oct 15th 2012, 09:24 AM
RD33
Re: This equation has two roots
Ok I got the answer 0 and 1/3 but how did you factor it. Where does the (1-3x) come from?
• Oct 15th 2012, 09:59 AM
Plato
Re: This equation has two roots
Quote:

Originally Posted by RD33
Ok I got the answer 0 and 1/3 but how did you factor it. Where does the (1-3x) come from?

Can you factor $3a^6b-9a^7b~?$ What do you get?