If one of the root of the quadratic equation is √ 5 - √3 ,

(vi) √ 5 - √3

Sol. If one of the root of the quadratic equation is √ 5 - √3 

 ,

then the other root is √ 5 + √3  

Let α= √ 5 - √3  and β= √ 5 + √3  

∴ α + β  = √ 5 - √3  + √ 5 + √3  = 2√5

and  α β  =  (√ 5 - √3  ) × (√ 5 + √3  )

= (√5)²  -  (√3)²

= 5 - 3

= 2

We know that, Quadratic equation is given by,

x² – (Sum of the roots)x + Product of the roots = 0

∴ x² –( α  + β)x + αβ = 0

∴ x² – (2√5)x + (2) = 0

∴  x² -  2√5x  + 2  = 0

∴  The required quadratic equation is  x² -  2√5x  - 2  = 0