# The equation of the smallest degree with real coefficients having $1+i$ as one of the roots is Option 1) $x^{2}+x+1=0$ Option 2) $x^{2}-2x+2=0$ Option 3) $x^{2}+2x+2=0$ Option 4) $x^{2}+2x-2=0$

As learnt in concept

To form a Quadratic Equation given the roots -

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

- wherein

S = Sum of roots

P = Product of roots

If 1+i is root

other root =1-i

sum=2

product =(1+i) (1-i)

=2

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

Option 1)

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

This option is incorrect

Option 2)

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

This option is correct

Option 3)

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

This option is incorrect

Option 4)

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

This option is incorrect

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