Answer:

It is given that, the polynomial equation of degree 4 having real coefficients with three of its roots as 2±

3

and 1+2i, so the remaining root is 1−2i.

Now, the quadratic equation whose roots as 2±

3

is

x

2

−4x+1=0, and

the quadratic equation whose roots as 1±2i, is

x

2

−2x+5=0

So, the required polynomial equation is

(x

2

−4x+1)(x

2

−2x+5)=0

⇒x

4

−6x

3

+14x

2

−22x+5=0

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