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Home » Math Homework Help » Algebra Homework Help » Reciprocal Roots
Reciprocal Roots
To transform an equation into another whose roots are the reciprocals of the roots of the given equation.

Let ƒ(x) = 0, then the equation of transformation is



and hence the transformed equation is



Thus the equation whose roots are reciprocals of the roots of the given equation is obtained by putting 1/x for x in the given equation.

Reciprocal equation: The equation ƒ(x) = 0 is said to be reciprocal if it remains unaltered when x is replaced by 1/x, i.e. in other words, the equation ƒ(x) = 0 is a reciprocal equation if



For example: x4 – 4x3 + 8x2 – 4x + 1 = 0, is a reciprocal equation.

The chief use of this transformation is to obtain the values of the expression which involve symmetric functions of the negative powers of the roots.

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