(v) ½ and – ½
Sol. The roots
of the quadratic equation are ½ and – ½ .
Let α = ½ and β =
- ½
∴ α + β = ½ + (– ½ )
= ½ – ½ = 0
and αβ = ½ × – ½ =
– ¼
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 – (0)x + (- ¼ ) = 0
Multiplying the equation with 4 we get,
∴ 4x2 + 0x – 1 = 0
∴ 4x2 – 1 = 0
∴ The required
quadratic equation is 4x2 – 1 = 0
