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