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# 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 toAnswer: 1 or 5

Ravi
6 years ago
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.
........................................................................................................................................
mycroft holmes
272 Points
6 years ago
Solution:$\text{Let} \ a \ \text{be the real root} \\ \\ \text{Then,} \ a^3+(3+i)a^2-3a-(m+i)= 0 \\ \\ \text{Comparing real and conjugate parts} \ a^3+3a^2-3a-m =0 \\ \\ \text{and} \ i(a^2-1)=0 \\ \\ \text{Hence, from second equation} \ a =\pm 1 \ \text{and therefore} \ m = 1,5 \\ \\$