Algebra Of Complex Numbers

It is given that, the polynomial equation of degree 4 having real coefficients with three of its roots as

2%20%5Cpm%20%5Csqrt%7B3%7D

and

1%2B2%20i

, so the remaining root is

1-2%20i

.
Now, the quadratic equation whose roots as

2%20%5Cpm%20%5Csqrt%7B3%7D

x%5E%7B2%7D-4%20x%2B1%3D0%2C

and
the quadratic equation whose roots as

1%20%5Cpm%202%20i

, is

x%5E%7B2%7D-2%20x%2B5%3D0

So, the required polynomial equation is

%5Cleft(x%5E%7B2%7D-4%20x%2B1%5Cright)%5Cleft(x%5E%7B2%7D-2%20x%2B5%5Cright)%3D0

%5CRightarrow%20x%5E%7B4%7D-6%20x%5E%7B3%7D%2B14%20x%5E%7B2%7D-22%20x%2B5%3D0

Chapter Questions
1 MCQs