Question

Please help? It’s the last problem and I’m stuck

Answer 1

x^2 - 4x + 5 = 0.

Explanation:

Note that the roots of (x - b)( x - c) = 0 are b and c, so:

We write it in factor form

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

Now expand:

x^2 - x(2 - i) - x(2 + i) -(2 + i)* - (2 - i) = 0

x^2 - 2x + ix - 2x - ix + (4 - 2i +2i - i^2)

x^2 - 4x + 4 + 1 = 0

x^2 - 4x + 5 = 0 (answer).