(Q5)Find the discriminant of the equation 3x2 - 2x +
1
3
 = 0 and hence find the nature of its roots. Find them, if they are real.

Here a = 3, b = -2 and c =
1
3
Therefore, discriminant b2 - 4ac = (-2)2 - 4 × ×
1
 = 4 - =.

Hence, the given quadratic equation has two equal real roots.

The roots are
-b
2a
,
-b
2a
 i.e
2
,
2
 i.e
1
,
1
 .