Hi Jaswant,

The text version of your answer

Find the roots of the quadratic equation √3x2 – 2√2 x – 2√3 = 0

√3x2 – 2√2 x – 2√3 = 0

Comparing equation with ax2 + bx + c = 0

Here, a = √3, b =  – 2√2 , c = –2√3

We know that

  D = b2 – 4ac

         = ("– 2" √2)^2– 4 ×(√3)×(-2√3)

         = (4 ×2)+8(√3  ×√3)

         = 8 + 8 × 3

            = 8 + 24

   = 32

So, the roots of the equation is given by

  x = (- b ± √D)/2a

Putting values

   x =  (- (- 2√2)  ± √32)/(2 × √3)

   x =  (2√2  ± √(16 × 2))/(2 × √3)

   x =  (2√2  ± √16  × √2)/(2√3)

   x =  (2√2  ± 4 √2)/(2√3)

   x =  (2√2  + 4√2)/(2√3)

   x =  (6√2)/(2√3) =  (3√2)/√3 = √3 ×  √2

   x = √(3 ×2) = √6

   x =  (2√2   - 4 √2)/(2√3)

   x =  (-2√2)/(2√3)

   x =  (-√2)/√3 = -√(2/3)

Hence, the roots of the equation are  √6 and -√(2/3).