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Question
`4sqrt3x^2+5x-2sqrt3=0`
Solution
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.
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