# An equation has roots 3 - i and 2 + i, what is the equation.

## Expert Answers There are an infinite number of equations that can have 3 - i and 2 + i as its roots. If the coefficients of the root are real, the simplest equation with roots 3 - i and 2 + i is one with highest degree 4. The other two roots of the equation are 3 + i and 2 - i. The equation is:

(x - (3 - i))(x - (2 + i))(x - (3 + i))(x - (2 - i)) = 0

=> (x - 3 + i)(x - 2 - i)(x - 3 - i)(x - 2 + i) = 0

=> ((x - 3)^2 - i^2)((x - 2)^2 - i^2) = 0

=> (x^2 + 9 - 6x + 1)(x^2 - 4x + 4 + 1) = 0

=> (x^2 + 10 - 6x)(x^2 - 4x + 5) = 0

=> x^4 - 10x^3 + 39x^2 - 70x + 50 = 0

The simplest equation with the given roots is x^4 - 10x^3 + 39x^2 - 70x + 50 = 0

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