Consider the equation z^2-(3+i) z+(m+2 i)=0 where m R . If the equation has exactly one real and one non real complex root, then which of the following hold(s) good?

Step-by-step solution

If is a real root then aligned & ^2-(3+i) +(m+2 i)=0 & ( ^2-3 +m )+i(2- ) & =2 and m=+2 aligned Now product of the root =m+2 i=2(1+i) [from the given equation] As real root is 2 aligned & non real root =1+ i & additive inverse =-1- i aligned (real root)(imaginary part of complex root) 2(1)=2