(i) 3 – 2√ 5
Sol. If one of
the root of the quadratic equation is 3 – 2√5 ,
then the other root is 3 + 2√ 5
Let α= 3 – 2√
5 and β
= 3 + 2√
5
∴ α + β = 3
– 2√ 5 + 3 + 2√ 5 = 6
and α β = (3 – 2√ 5) × (3 + 2√ 5)
= (3)2 –
(2√ 5)2
= 9 – 4 × 5
= 9 – 20
= – 11
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 – (6)x + (-11) = 0
∴ x2 - 6x - 11 =
0
∴ The required
quadratic equation is x2 - 6x - 11 =
0
