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  • Confused! kindly explain, - Complex numbers and quadratic equations - JEE Main-4

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

x = 1 is a root by observation, which is a rational root.

Since all coefficients will be rational so irrational root can't occur alone, hence other root will also be 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

Posted by

divya.saini

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