# Thread: Roots of oolynomial equations

1. ## Roots of oolynomial equations

Sorry if this is in the wrong section. I wasn't sure where it went!
If you have an equation:
$\displaystyle x^2 + 4x + 7 = 0$
Which has roots
$\displaystyle \alpha and \beta$
And you want an equation that has roots
$\displaystyle \alpha + 2\beta and \beta + 2\alpha$

$\displaystyle let u = \alpha + 2\beta$
Im going to get alpha in terms of beta and u...and if i sub this into the equation im going to still have beta :S...
I know you can do it via sum of roots = -b/a etc but im told in this example to use substitution -,-.

Thanks.

2. Originally Posted by AshleyT
Sorry if this is in the wrong section. I wasn't sure where it went!
If you have an equation:
$\displaystyle x^2 + 4x + 7 = 0$
Which has roots
$\displaystyle \alpha and \beta$
And you want an equation that has roots
$\displaystyle \alpha + 2\beta and \beta + 2\alpha$

$\displaystyle let u = \alpha + 2\beta$
Im going to get alpha in terms of beta and u...and if i sub this into the equation im going to still have beta :S...
I know you can do it via sum of roots = -b/a etc but im told in this example to use substitution -,-.

Thanks.
You don't, you use the information that if $\displaystyle a$ and $\displaystyle b$ are roots of $\displaystyle x^2+ux+v$ then $\displaystyle u=a+b$ and $\displaystyle v=ab$.

CB

3. Originally Posted by CaptainBlack
You don't, you use the information that if $\displaystyle a$ and $\displaystyle b$ are roots of $\displaystyle x^2+ux+v$ then $\displaystyle u=a+b$ and $\displaystyle v=ab$.

CB
Yeah , but annoyingly im not allowed to use that method in this question ..I have to use a substitution method.