IIT JEE , AIEEE Forum - Mathematics , Algebra

shreyaarya

what are extraneous roots?

naughtygal

If u get a set of root fr an equation den all other roots ,xpect fr which the eqation becomes zero , r called extraneous roots.
Hope it will help.

karansingh

When you multiply both sides of an equation by an expression which
includes the variable, you run the risk of introducing extraneous
roots. Let me give a very simple example. Suppose you have the
equation

x = 3

for which the solution is obviously 3. Now multiply both sides of
this equation by x which gives

x² = 3x

One of the roots of this equation is still 3, but there is also
another root, namely zero, which has been introduced. {0,3} are roots
of the second equation, but only 3 is a root of the first. Often, in
the process of solving radical equations, we square both sides -
the equivalent of multiplying by an expression which includes the
variable. We find roots to this new equation, but sometimes not all
roots of the new equation are also roots of the original equation.
I hope that this helps.

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