4 – 3√ 2

(ii) 4 – 3√ 2

Sol. If one of the root of the quadratic equation is 4 – 3√2 ,

then the other root is 4 + 3√ 2

Let α= 4 – 3√2 and β  = 4 + 3√2

∴ α + β  = 4 – 3√2 + 4 + 3√2 = 8

and  α β  =  (4 – 3√2) × (4 + 3√2)

= (4)²  –  (3√ 2)²

= 16 – 9 × 2

= 16 – 18

= – 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 – (8)x + (-2) = 0

∴  x² -  8x  - 2  = 0

∴  The required quadratic equation is  x² -  8x  - 2  = 0