How to Find the Equation for a Quadratic with a Root of 1 + 3i?

[suganya]

Hi,

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

Regards,
Suganya

EasyCalculation
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[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 don't 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.

 

[HallsofIvy]

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!