Question

`2sqrt3x^2-5x+sqrt3=0`

Answer 1

The given equation is` 2sqrt3x^2-5x+sqrt3=0` 

Comparing it with `ax^2+bx+c=0` we get 

`a=2sqrt3, b=-5 and c=sqrt3` 

∴ Discriminant, `D=b^2-4ac=(-5)^2-4xx2sqrt3xxsqrt3=25-25=1>0`  

So, the given equation has real roots.
Now, `sqrtD=sqrt1=1` 

∴` α=(-b+sqrt(D))/(2a)=(-(-5+1)+1)/(2xx2sqrt3)=6/(4sqrt3)=sqrt3/2` 

`β=(-b-sqrt(D))/(2a)=(-(-5)-1)/(2xx2sqrt3)=4/(4sqrt(3))=sqrt(3)/3` 

Hence, `sqrt3/2` and `sqrt3/3`are the roots of the given equation.