½ and – ½

(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