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Question

The equation of the smallest degree with real coefficients having 1 + i as one of the roots is
(a) x2+x+1=0
(b) x2-2x+2=0
(c) x2+2x+2=0
(d) x2+2x-2=0

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Solution

(b) x2-2x+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,

x2-1+i+1-ix+1+i1-i=0x2-2x+2=0

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