Find the nature of the roots of the quadratic equation `3x^(2)-4sqrt(3)x+4=0` and hence solve it.

Explanation

This is of the form `ax^(2)+bx+c=0,` where a=3, `b=-4sqrt(3)` and c=4.
`:." "D=(b^(2)-4ac)={(-4sqrt(3))^(2)-4xx3xx4}=(48-48)=0.`
This shows that the given quadratic equation has real and equal roots.
Each root `=(-b)/(2a)=(4sqrt(3))/(6)=(2sqrt(3))/(3).`
Hence, `(2sqrt(3))/(3)" and "(2sqrt(3))/(2)` are the roots of the given equation.