Get Answers to all your Questions

header-bg qa

If  2+3is one of the roots of the equation 2x^{3}-9x^{2}+kx-13=0,\: \: k\epsilon R, then the real root of this equation :

  • Option 1)

     does not exist.

  • Option 2)

    exists and is equal to \frac{1}{2}

  • Option 3)

    exists and is equal to -\frac{1}{2}

  • Option 4)

    exists and is equal to 1

 

Answers (2)

best_answer

As we have learned

Sum of roots of cubic Equation -

\alpha +\beta +\gamma = \frac{-b}{c}

 

- wherein

ax^{3}+bx^{2}+cx+d= 0

is the cubic equation

 

 

Product of roots of cubic equation -

\alpha \beta \gamma = \frac{-d}{a}

- wherein

ax^{3}+bx^{2}+cx+d= 0

is the cubic equation

 

 \alpha = 2+3 ;

\beta = 2-3 ;

\gamma = ?

 

\alpha +\beta +\gamma = 9/2

and     \alpha\beta\gamma = 13/2

 (4+9)\gamma = 13/2

\gamma = 1/2

 

 

 

 

 

 


Option 1)

 does not exist.

Option 2)

exists and is equal to \frac{1}{2}

Option 3)

exists and is equal to -\frac{1}{2}

Option 4)

exists and is equal to 1

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE