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The quadratic equation whose roots are $(2 + i)$ and $(2 - i)$ is

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x^{2} + 4 x + 5 = 0

x^{2} + 4 x - 5 = 0

x^{2} - 4 x + 5 = 0

x^{2} - 4 x - 5 = 0

answer is C.

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Detailed Solution

Let

α = 2 + i, β = 2 - i

Sum of the roots $α + β = 2 + i + 2 - i$

$α + β = 4$

Product of the roots $α β = (2 + i) (2 - i)$

$α β = 2^{2} - i^{2}$

$α β = 4 + 1$

$α β = 5$

Quadratic equation is $x^{2} - x (α + β) + α β = 0$

$x^{2} - 4 x + 5 = 0$

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