(2 + i)x² – (5 – i)x + 2(1 – i) = 0

Given (2 + i)x² – (5 – i)x + 2(1 – i) = 0

Recall that the roots of quadratic equation ax² + bx + c = 0, where a ≠ 0, are given by

Here, a = (2 + i), b = –(5 – i) and c = 2(1 – i)

By substituting i² = –1 in the above equation, we get

We can write –2i = –2i + 1 – 1

⇒ –2i = –2i + 1 + i² [∵ i² = –1]

⇒ –2i = 1 – 2i + i²

⇒ –2i = 1² – 2(1)(i) + i²

⇒ –2i = (1 – i)² [∵ (a – b)² = a² – 2ab + b²]

By using the result –2i = (1 – i)², we get

[∵ i² = –1]

Thus, the roots of the given equation are 1 – i and.