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  • Help me understand! - Complex numbers and quadratic equations - JEE Main-6

One root of quadratic equation with rational coefficients is 1-\sqrt{2} then quadratic will be

  • Option 1)

    x^{2}-2x-1= 0

  • Option 2)

    x^{2}+2x-1= 0

  • Option 3)

    x^{2}-x-2= 0

  • Option 4)

    x^{2}+x-2= 0

 

Answers (1)

best_answer

One root is 1-\sqrt{2} so other will be 1+\sqrt{2} 

\therefore Sum = 2 and product = -1

\therefore x^{2}-2x-1=0 will be equation

\therefore Option (A)

 

Nature of roots (Irrational) -

a,b,c\in Q ( Rational no.)

If P+\sqrt{q}\left ( P,q \in Q \right ) is an irrational root

\Rightarrow P-\sqrt{q} is also a root

- wherein

ax^{2}+bx+c=0

is a quadratic equation

 

 


Option 1)

x^{2}-2x-1= 0

This is correct

Option 2)

x^{2}+2x-1= 0

This is incorrect

Option 3)

x^{2}-x-2= 0

This is incorrect

Option 4)

x^{2}+x-2= 0

This is incorrect

Posted by

Plabita

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