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. The additive inverse of non-real root, is
A
1−i
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B
1+i
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C
−1−i
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D
−2
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Solution
The correct option is C−1−i z2−(3+i)z+m+2i=0 Let α be the real root. Then, α2−(3+i)α+m+2i=0 ⇒(α2−3α+m)+i(2−α)=0+i⋅0 ∴α−2=0 and α2−3α+m=0 ⇒α=2 and m=2 Now, product of the roots =2(1+i) with one root as 2 So, non-real root =1+i ∴ Additive inverse is −1−i