The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x^2 – 11x + α = 0 are rational numbers is:

Question

Accepted Answer

Correct answer: A. (a) For the roots of quadratic equation ax^2+ bx+c=0 to be rational D=(b^2-4 ac) should be perfect square. In the equation 6x^2-11x+ =0 ∴ For root to be rational D= (-11 )^2-4 (6 ) ( ) should be a perfect square. ⇒D ( )=121-24 should be a perfect square Now, D (1 )=121-24=97 is not a perfect equare. D (2 )=121-24 2=73 is not a perfect square. D (3 )=121-24 3=49 is a perfect square. D (4 )=121-24 4=25 is a perfect square. D (5 )=121-24 5=1 is a perfect square. and for 6 ,D ( )<0, hence imaginary roots. ∴ For 3 values of ( =3 ,4 ,5 ), the roots are rational.

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

Solution

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