Math CentralQuandaries & Queries


Question from Tiffany, a student:

Find the quadratic equation with roots at (3-i) and its complex conjugate.

Hi Tiffany,

If I asked you to find the quadratic equation with roots 3 and -2 could you find it? I think you could. Since the quadratic has roots 3 and -2 it would factor as (x - 3)(x + 2) and expanding this gives x2 -x -6.

The question you sent us asks to find the quadratic with roots 3 - i and its complex conjugate 3 + i. Using the same technique this quadratic is (x - [3 - i])(x - [3 + i]) = (x - 3 + i)(x - 3 - i). Expand this expression. When you have the quadratic in standard form you can use the general quadratic or complete the square to find the roots which should be 3 - i and 3 + i.


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