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

 

Answers (1)

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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