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  • Answer please! - Complex numbers and quadratic equations - JEE Main-2

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

  • Option 1)

    0

  • Option 2)

    1

  • Option 3)

    2

  • Option 4)

    Can't be determined.

 

Answers (1)

best_answer

By observation we see x = 1 is one of the roots which is a rational root and it is given a,b,c\, \epsilon \, Q so all coefficients are rational hence irrational root can't come alone , So other root will be also rational.

\therefore Option (C)

 

Nature of Rational roots -

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

- wherein

Sometimes one root is observed by observation and with this concept nature of other root can be decided.

 

 


Option 1)

0

This is Incorrect

Option 2)

1

This is Incorrect

Option 3)

2

This is correct

Option 4)

Can't be determined.

This is Incorrect

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Aadil

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