If the equation z³ +(3+i)z²-3z- (m+i)=0, where m is a real number, has at least one real root, then m can have the value equal to


Answer: 1 or 5

Let a,b,c be the roots.
If a is real, (b,c are conjugates)
a+b+c=3+i
abc=m+i
ab+bc+ca=-3

Use this information and solve for m.
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