- 3 and –11

(iii) - 3 and –11

Sol. The roots of the quadratic equation are -3  and – 11.

Let α  = -3 and β  = - 11

∴  α  + β  = -3 + (–11) = -3 – 11 = – 14

and αβ  = - 3  × – 11 =  33

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 – (–14)x + ( 33) = 0

∴  x² + 14x  33 = 0

∴  The required quadratic equation is x² + 14x  33 = 0