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If a+b\neq 2c   and  a,b,c\; \epsilon \; Q  then the number of rational roots of equation \left ( a+b-2c \right )x^{2}+\left ( b+c-2a \right )x+\left ( c+a-2b \right )= 0  equals

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

Can't be determined.


Answers (1)

best_answer

As we learnt in

Nature of roots

If   P\left ( x \right )= 0  is a polynomial equation with rational coefficients then irrational roots always occur in pair.

 

Now,

As the sum of coefficients is 0, so x = 1 is a root. So one root is rational.

Now, since all coefficients are rational, and irrational root can occur in pairs only for such a case, and one root is rational (x=1), hence other root will also be rational.

\therefore Option (C)

Posted by

Pankaj

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