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Question

Find the equation whose roots are equal in magnitude but opposite in sign to the roots of the equation x5- 3 x3 + 2 x2 + 4x + 1 = 0.


A

x5+ x3 + x2 + x + 1 = 0

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B

x5 - 3x3 - 2x2 + 4x - 1 = 0

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C

x5 + 2x3 + 3x2 + 5x - 1 = 0

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D

x5- 3x3 + 2x2 + 4x + 1 = 0

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Solution

The correct option is B

x5 - 3x3 - 2x2 + 4x - 1 = 0


Solution: x5- 3 x3 + 2 x2 + 4x + 1 = 0 ____ (1)

Let x be a root of the given equation and y a root of the required equation.

Then y = - x or x = - y

Put x = - y in the equation 1, we have

- y5 + 3 y3 + 2 y2 - 4y + 1 = 0

Express it in terms of x

- x5 + 3 x3 + 2 x2 - 4x + 1 = 0

x5 - 3 x3 - 2 x2 + 4x - 1 = 0


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