(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
