Question

Let $z$ be a complex number satisfying the equation $z^2-(3+i)z+m+2i=0$, where $mϵR$. Suppose the equation has a real root, then the value of $m$ is

• A. -1
• B. -2
• C. 2
• D. 1

Answer 1

The correct option is C 2

Given: equation $z^2-(3+i)z+m+2i=0$, where $z$ is complex number, $m\in R$

To find the value of $m$ if the equation has real root

Solution:

$z^2-(3+i)z+m+2i=0$

Let $\alpha$ be the real root, then according to given condition it should satisfy the given equation.

i.e., ${\alpha }^2-3\alpha -i\alpha +m+2i=0⟹({\alpha }^2-3\alpha +m)+i(2-\alpha )=0$

Now by equating real and imaginary part to zero, we get

${\alpha }^2-3\alpha +m=0$ and $\alpha =2$

By putting $\alpha =2$ in ${\alpha }^2-3\alpha +m=0$, we get

$4-3\left(2\right)+m=0⟹m=2$