√ 2 + √3

(iii) √ 2 + √3


Sol. If one of the root of the quadratic equation is √2 +√3 ,


then the other root is √2 – √3

Let α= √2 + √3and β= √2 - √3

∴ α + β  = √2 + √3+ √2 -  √3 = 2√2

and  α β  =  (2 + √3) × (√2 - √3)

= (√2 )2  –  (√3)2

= 2 – 3

= – 1

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√2)x + (-1) = 0

 x2 -  2√2x  - 1  = 0


 The required quadratic equation is  x2 -  2√2x  - 1  = 0