If the equation, x2 + bx + 45 = 0 (b \in R) has conjugate complex roots and they satisfy \left|\right. z + 1 \left|\right. \textrm{ } = 2 \sqrt{10}, then :

Engineering

Mathematics

Geometry of Complex Number

Question

If the equation, x² + bx + 45 = 0 (b $\in$ R) has conjugate complex roots and they satisfy $| z + 1 | = 2 \sqrt{10}$ , then :

b² – b = 42

b² + b = 72

b² – b = 30

b² + b = 12

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Let z = α ± iβ be roots of the equation

So 2α = –b and α² + β² = 45, (α + 1)² + β² = 40

So (α + 1)² – α² = – 5

⇒ 2α + 1 = – 5 ⇒ 2α = – 6

so b = 6

hence b² – b = 30