The complex number 1 + 2I is a root of the equation x ^ 2 + BX + C = 0 (B, C belong to R)

The complex number 1 + 2I is a root of the equation x ^ 2 + BX + C = 0 (B, C belong to R)

1 + 2I is a root of the equation x ^ 2 + BX + C = 0 (B, C belongs to R)
The other root is 1-2i
-b=1+2i+1-2i=2
b=-2
c=(1+2i)(1-2i)
=1+4
=5

If an imaginary root of quadratic equation with real coefficients is 5 / 1 + 2I, then B = C=

5/(1+2i)
=5(1-2i)/(1+4)
=1-2i
The two imaginary roots of quadratic equation with real coefficients are conjugate complex numbers
The other one is 1 + 2I
According to Weida's theorem
-b=1-2i+1+2i=2
∴b=-2
c=(1-2i)(1+2i)=1+4=5