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  • Solve it, - The number of all possible positive integral values of for which the roots of the quadratic equatio - Complex numbers and quadratic equations - JEE Main

The number of all possible positive integral values of \alpha for which the roots of the quadratic equation,6x^{2}-11x+\alpha =0 are rational number is:

  • Option 1)

     

    4

  • Option 2)

     

    3

  • Option 3)

     

    2

  • Option 4)

     

    5

Answers (1)

best_answer

 

Condition for Rational roots of quadratic equation -

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

D= b^{2}-4ac   is a perfect square of rational no.

- wherein

ax^{2}+bx+c=0

is a quadratic equation

 

 

Given quadratic equation

6x^2 - 11x +\alpha

from the concept of rational roots 

\Rightarrow D = must be perfect square

\Rightarrow 121-4\times 6\times \alpha = \lambda^2

Maximum value of \alpha = 5 

\\\alpha = 1 \Rightarrow \lambda \notin I \\\alpha = 2 \Rightarrow \lambda \notin I \\\alpha = 3 \Rightarrow \lambda \in I \\\alpha = 4 \Rightarrow \lambda \in I \\\alpha = 5 \Rightarrow \lambda \in I

\Rightarrow 3 \;\textup{Integers}


Option 1)

 

4

Option 2)

 

3

Option 3)

 

2

Option 4)

 

5

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