Publish On: 2019-03-23

# jollay

Total Post: 559

## Question: Describe the roots with signs changed

Reply On: 2013-10-08

# Mjay Jollay

Total Post: 0

## ANS: Describe the roots with signs changed

To transform an equation into another whose roots are those of the proposed equation with contrary signs.

Let be the roots of the given equation and are the roots of the new equation Ø(y) = 0.

Since

and satisfies

Ø(y) = 0

Also, x = , satisfies

ƒ(x) = 0

therefore, equation of transformation is

y = -x or x = -y

Substituting this value of x in ƒ(x) = 0, we get the transformed equation ƒ(-y) = 0.

Hence Ø(y) = ƒ(-y).

Obviously, if ƒ(x) = a

then the required equation is

a

or, a

Let be the roots of the given equation and are the roots of the new equation Ø(y) = 0.

Since

and satisfies

Ø(y) = 0

Also, x = , satisfies

ƒ(x) = 0

therefore, equation of transformation is

y = -x or x = -y

Substituting this value of x in ƒ(x) = 0, we get the transformed equation ƒ(-y) = 0.

Hence Ø(y) = ƒ(-y).

Obviously, if ƒ(x) = a

_{0}x^{n}+ a_{1}x^{n-1}+ ….. + a_{n}= 0, a_{n}≠ 0,then the required equation is

a

_{0}y^{n}– a_{1}y^{n-1}+ …. + (-1)^{n-1}a_{n-1 }y + (-1)^{n}a_{n}= 0or, a

_{0}x^{n}– a_{1}x^{n-1}+ …. + (-1)^{n-1}a_{n-1 }x + (-1)^{n}a_{n}= 0.Like Us On Facebook for All Latest Updates