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Roots of the equation x2 + bx + 45 = 0, b ∈ R lie on the curve |z + 1| = 2√10, where z is a complex number then(1) b2 + b = 12 (2) b2 – b = 30 (3) b2 – b = 36 (4) b2 + b = 30 |
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Answer» Answer is (2) b2 – b = 30 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 |
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