Question

The quadratic equation with real co-efficients having one root $\frac{1}{2}(1+\sqrt{-3})$ is

• A. $x^2-x-1=0$
• B. $x^2+x-1=0$
• C. $x^2+x+1=0$
• D. $x^2-x+1=0$

Answer 1

The correct option is D $x^2-x+1=0$

If one root is $\frac{1+i\sqrt{3}}{2}$, the other root is $\frac{1-i\sqrt{3}}{2}$.

So, sum of roots $=\frac{1+i\sqrt{3}}{2}+\frac{1-i\sqrt{3}}{2}=1$.

And product of roots $=\left(\frac{1+i\sqrt{3}}{2}\right)\left(\frac{1-i\sqrt{3}}{2}\right)=\frac{4}{4}=1$.

Hence, equation is $x^2-x+1=0$.