The equation of the smallest degree with real coefficients having 1 + i as one of the roots is

$x^{2} + x + 1 = 0$

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$x^{2} 2 x + 2 = 0$

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$x^{2} + 2 x + 2 = 0$

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

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Solution

The correct option is B
$x^{2} 2 x + 2 = 0$

We know that, imaginary roots of a quadratic equation occur in conjugate pair.

It is given, that, 1 + i is one of the roots.

So, the other root will be 1 - i.

Thus, the quadratic equation having roots 1 + i and 1-i is,

$x^{2} - (1 + i + 1 - i) x + (1 + i) (1 - i) = 0 \Rightarrow x^{2} - 2 x + 2 = 0$

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