Question

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

विकल्प

• $$x^2+x+1=0$$

• $$x^2-2x+2=0$$

• $$x^2+2x+2=0$$

• $$x^2+2x-2=0$$

Answer 1

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

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,

$$x^2-(1+i+1-i)x+(1+i)(1-i)=0$$

$$\Rightarrow x^2-2x+2=0$$