1. Aug 8, 2007

### suganya

Hi,

How to find the equation if one root of a quadratic equation is 1 + 3i.

Regards,
Suganya

EasyCalculation
ToFocus

2. Aug 8, 2007

### Gib Z

Does the equation has real co efficients? If it does, the other root is the complex conjugate of that root. If not, and you have the co efficients which I dont think you do, then just set (x - your root) as a factor and divide. If you don't know any of that information, no way to tell.

Last edited: Aug 8, 2007
3. Aug 8, 2007

### HallsofIvy

Staff Emeritus
Your "find the equation" implies that there is only one such equation. There isn't. If a quadratic equation has x0 and x1 as roots, then it must be of the form a(x-x0)(x- x1)= 0 where a can be any number.

You know that one root is 1+ 3i. As Gib Z said, if your equation must have real coefficients, then the other root must be its complex conjugate 1- 3i so any equation of the form a(x- 1- 3i)(x- 1+ 3i)= 0 will work. If you do not require real coefficients, choose any complex number at all for the second root!

Last edited: Aug 8, 2007