Let a, b be real and z be complex number. If z2 + az + b = 0 has two distinct roots on the line Re z = 1, then it is necessary that :

Engineering

Mathematics

Conjugate Modulus and Argument of a Complex Number

Question

Let a, b be real and z be complex number. If z² + az + b = 0 has two distinct roots on the line Re z = 1, then it is necessary that :

b $\in$ (0, 1)

| b | = 1

b $\in$ (1, $\infty$ )

b (–1, 0)

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Let roots be p + iq and p – iq p, q $\in$ R

root lie on line Re(z) = 1

$\Rightarrow$ p = 1

product of roots = p² + q² = b = 1 + q²

$\Rightarrow$ b $\in$ (1, $\infty$ ), (q $\neq$ 0, Q roots are distinct)

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