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Home » Math Homework Help » Algebra Homework Help » Transformation in General
Transformation in General
Let ƒ(x) = 0 be a given equation whose roots are connected by the given relation F(x, y) = 0, known as the equation of transformation. Then the transformed equation Ø(y) = 0 is obtained by eliminating x from ƒ(x) = 0 and F(x, y) = 0.

Example: if , , are the roots of the equation

x3 – px2 + qx = 0,

form an equation whose roots are





Now, , , are the roots of the equation

x3 – px2 + qx – r = 0                       (1)

= r



Since x = is the root of the equation (1), hence the relation of transformation is



Or, ry3 – q(1 + r)y2 + p(1 + r)2y – (1 + r)3 = 0

Or, rx3 – q(1 + r)x2 + p(1 + r)x = (1 + r)3 = 0

is the required equation.

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