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Find the discriminant of the equation `3x^2-2x+1/3=0`and hence find the nature of its roots. Find them, if they are real.

Answer» Here, equation is , `3x^2-2x+1/3 = 0`
Comparing it with, `ax^2+bx+c = 0`
`a = 3, b = -2 and c = 1/3`
So, discriminant,`(d) = sqrt(b^2-4ac)`
`d = sqrt((-2)^2-4(3)(1/3)) = 0`
We know, if `d >=0`, roots are real and if `d<0`, roots are unreal.Here, as `d = 0`, roots are real and equal.Now, roots are` = (-b+-sqrt(d))/(2a) = -b/(2a) = 1/3`So, roots are `(1/3,1/3)`


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