2√3 – 4

(iv) 2√3 – 4

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

then the other root is 2√ 3 + 4

Let α= 2√ 3 – 4and β= 2√ 3 + 4

∴ α + β  = 2√ 3 – 4+ 2√ 3 + 4= 4√3

and  α β  =  (2√ 3 – 4) × (2√ 3 + 4)

= (2√3 )²  –  (4)²

= 4× 3 – 16

= 12 – 16

= - 4

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 – (4√3)x + (-4) = 0

∴  x² -  4√3x  - 4  = 0

∴  The required quadratic equation is  x² -  4√3x  - 4  = 0