(v) 2+√5
Sol. If one of
the root of the quadratic equation is 2+√5
,
then the other root is 2 - √5
Let α= 2+√5 and β= 2 - √5
∴ α + β = 2+√5 +
2 - √5 = 4
and α β = (2+√5 ) × (2 - √5 )
= (2)2 –
(√5)2
= 4 – 5
= - 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 – (4)x + (-1) = 0
∴ x2 - 4x - 1 = 0
∴ The required
quadratic equation is x2 - 4x - 1 = 0
