The number of all possible positive integral value of α for which the roots of the quadratic equation 6…

The number of all possible positive integral value of α for which the roots of the quadratic equation 6x2-11x+α=0 are rational numbers is:
  1. 5
  2. 3
  3. 4
  4. 2

Solution

For ax2+bx+c=0, we have D=b2-4ac 

D=121-24α
For rational roots, D must be perfect square.
∴α=3, 4, 5
∴ Number of values of α=3

Asked in: JEE Main 2019 (09 Jan Shift 2)

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