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a= sqrt 3 and b= 3/4, when the euation has real and equal roots then D=0 ie b^2-4ac=0, we know that b=a, a=1 and c=b then by substituting we get a^2-4b=0, ie a^2=4b-----------(1)
we are given that sum of roots= -a and product = -6 let x and y be the roots then x+y=-a and xy= -6 and also we are given that x= sqrt3 so by substituting we get a= sqrt 3 and by substituting this value in eq (1) above we get b= 3/4
in the first equation we r already given one root so we find out the other root and in the second equation its given that the roots are real and equal so D which is the discriminant= 0 and we know that D=b^2-4ac for a quad eq of the form ax^2 + bx +c =0