½ and – ¾

(ii) ½  and – ¾  

Sol. The roots of the quadratic equation are ½  and – ¾ .

Let α  = ½  and β  = - ¾

∴  α  + β  = ½  + (–  ¾ ) = ½ - ¾  = – ¼

and αβ  = ½ × - ¾ = - 3/8

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 – (– ¼ )x + (– 3/8) = 0

Multiplying the above equation with 8, we get

 8x2 + 2x – 3 = 0


 The required quadratic equation is 8x2 + 2x – 3 = 0