x = (2 + i) and (2 - i) are the roots of the quadratic equation f(x) = x² - 4x + 5.
What are roots of a quadratic equation?
The values of variables satisfying the given quadratic equation are called its roots.
Given (2 + i) and (2 - i) are roots of the quadratic equation.
Let the quadratic equation be f(x).
(x - (2 + i)) and (x - (2 -i)) are the factors of f(x).
Since, f(x) is a quadratic equation, it has only two roots.
f(x) = (x - (2 + i))(x - (2 - i))
f(x) = x² - (2 - i)x - (2 + i)x + (2 - i)(2 + i)
f(x) = x² - 2x + ix - 2x - ix + 4 - i²
f(x) = x² - 4x + 4 + 1
f(x) = x² - 4x + 5
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