Grade 11IIT JEE Entrance Exam
If all the roots of z^3+az^2+bz+c=0 are of unit modulus , then prove that mod a ≤3.
If all the roots of z^3+az^2+bz+c=0 are of unit modulus , then prove that mod a ≤3.
1 Answer
Vijay Mukati
Dear Student,
Sum of roots will be equal to -a.
Thus Modulus (alpha + beta + gamma) = a
Modulus(alpha) + Modulus(beta) + Modulus(gamma) = a
Therefore Modulas(a) = 3.
Sum of roots will be equal to -a.
Thus Modulus (alpha + beta + gamma) = a
Modulus(alpha) + Modulus(beta) + Modulus(gamma) = a
Therefore Modulas(a) = 3.
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