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