Quadratic Equation

suganya

Hi,

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

Regards,
Suganya

EasyCalculation
ToFocus

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.

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!