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Question

# If α, β, γ and δ are the roots of x4 + 2 x3 + 3 x2 + 4x + 5 = 0. Find the equation whose roots are 1α, 1β, 1γ, 1δ

A

x4 - 2x3 + 3x2 - 4x + 5 = 0

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B

x4 + 3x3 + 2x2 + 4x + 5 = 0

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C

5x4 + 4x3 + 3x2 + 2x + 1 = 0

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D

5x4 - 4x3 + 3x2 - 2x + 1 = 0

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Solution

## The correct option is C 5x4 + 4x3 + 3x2 + 2x + 1 = 0 Roots of x4 + 2 x3 + 2 x2 + 4x + 5 = 0 ---------------------(1) are α, β, γ, δ Changing x to 1x 1x4 + 2x3 + 3x2 + 4x + 5 = 0 5 x4 + 4 x3 + 3 x2 + 2x + 1 = 0 _________(2) Roots of the equation 2 being the reciprocal of equation 1. 1α, 1β, 1γ, 1δ

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