Thread: Find 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.

Originally Posted by carmo100

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.

This is a nice, little theorem (a particular case of Viete's formulae):

Theorem: if are the roots of a quadratic equation , then

Tonio

Thankyou, this is exactly what I needed.

Also, any quadratic having roots and is of the form . Replace with -3+ 2i, 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)