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Question

Let z be a complex number satisfying the equation z2(3+i)z+m+2i=0, where mϵR. Suppose the equation has a real root, then the value of m is

A
-1
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B
-2
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C
2
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D
1
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Solution

The correct option is C 2
Given: equation z2(3+i)z+m+2i=0, where z is complex number, mR
To find the value of m if the equation has real root
Solution:
z2(3+i)z+m+2i=0
Let α be the real root, then according to given condition it should satisfy the given equation.
i.e., α23αiα+m+2i=0(α23α+m)+i(2α)=0
Now by equating real and imaginary part to zero, we get
α23α+m=0 and α=2
By putting α=2 in α23α+m=0, we get
43(2)+m=0m=2

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