Question

`4sqrt3x^2+5x-2sqrt3=0` 

Answer 1

The given equation is `4sqrt3x^2+5x-2sqrt3=0`   

Comparing it with` ax^2+bx+c=0` 

`a=4sqrt(3),b=5 and c=-2sqrt3` 

∴ Discriminant, `D=b^2-4ac=5^2-4xx4sqrt3xx(-2sqrt3)=25+96=121>0` 

So, the given equation has real roots.
Now, `sqrtD=sqrt(121)=11` 

∴ `α =(-b+sqrt(D))/(2a)=(-5-11)/(2xx4sqrt(3))=6/(8sqrt(3))=sqrt3/4` 

β=`(-b-sqrt(D))/(2a)=(-5-11)/(2xx4sqrt(3))=-16/(8sqrt(3))=(2sqrt(3))/3` 

Hence, `sqrt3/4` and `(-2sqrt3)/3` are the root of the given equation.