I was wondering how to go about doing this question:

Findallquadratics with the roots -3+-2i in the form ax^2 +bx+c=0

any help is appreciated.

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- Jan 27th 2010, 01:47 AMcarmo100Find quadratic using its roots.
I was wondering how to go about doing this question:

Find*all*quadratics with the roots -3+-2i in the form ax^2 +bx+c=0

any help is appreciated. - Jan 27th 2010, 01:54 AMtonio
- Jan 27th 2010, 02:01 AMcarmo100
Thankyou, this is exactly what I needed.

- Jan 27th 2010, 02:34 AMHallsofIvy
Also, any quadratic having roots $\displaystyle r_1$ and $\displaystyle r_2$ is of the form $\displaystyle a(x- r_1)(x+ r_1)= 0$. Replace $\displaystyle r_1$ with -3+ 2i, $\displaystyle r_2$ with -3- 2i, and multiply that out.

The easiest way to do that is to think of it as a product of "sum and difference": ((x-3)- 2i)((x-3)+ 2i)