Let z be a complex number satisfying the equation z2-3-iz-m-2i-0- where m- R- Suppose the equation has a real root- Then find the non-real root-

Let Z be a complex Numbers satisfying the equation $z^{2}$ - (11 + i) z+k+3i = 0 where k $ϵ$ R and i = $\sqrt{(- i)}$ , suppose equation has one real and one non-real root. Find the non-real root.

Q. If the equation

Z^{2} - (3 + i) z + m + 2i = 0,m \in R

has a real root, then the value of m is

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Let z be a complex number satisfying the equation z2−(3+i)z+m+2i=0, where m∈R. Suppose the equation has a real root. Then find the non-real root.

The correct option is C 1+iLet α be the real root. Then,α2−(3+i)α+m+2i=0or (α2−3α+m)+i(2−α)=0or α=2 or 4−6+m=0 or m=2Product of the roots is 2(1+i) with one root as 2. Hence, the nonreal root is 1+i.Ans: C

Let $z$ be a complex number satisfying the equation $z^{2} - (3 + i) z + m + 2 i = 0$ , where $m \in R$ . Suppose the equation has a real root. Then find the non-real root.

The correct option is C $1 + i$
Let $α$ be the real root. Then,
$α^{2} - (3 + i) α + m + 2 i = 0$
or $(α^{2} - 3 α + m) + i (2 - α) = 0$
or $α = 2$ or $4 - 6 + m = 0$ or $m = 2$
Product of the roots is $2 (1 + i)$ with one root as 2.
Hence, the nonreal root is $1 + i$ .
Ans: C