Publish On: 2019-03-24

# jollay

Total Post: 559

## Question: Explain the transformation in general

Reply On: 2013-10-08

# Mjay Jollay

Total Post: 0

## ANS: Explain the 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

x

form an equation whose roots are

Now, are the roots of the equation

x

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

Or, ry

Or, rx

is the required equation.

Example: if are the roots of the equation

x

^{3}– px^{2}+ qx = 0,form an equation whose roots are

Now, are the roots of the equation

x

^{3}– px^{2}+ qx – r = 0 (1)Since x = is the root of the equation (1), hence the relation of transformation is

Or, ry

^{3}– q(1 + r)y^{2}+ p(1 + r)^{2}y – (1 + r)^{3}= 0Or, rx

^{3}– q(1 + r)x^{2}+ p(1 + r)x = (1 + r)^{3}= 0is the required equation.

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