5 and – 7

(i) 5 and – 7

Sol. The roots of the quadratic equation are 5 and – 7.

Let α  = 5 and β  = - 7

∴  α  + β  = 5 + (– 7) = 5 – 7 = – 2

and αβ  = 5 × – 7 = – 35

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 – (– 2)x + (– 35) = 0

∴  x² + 2x – 35 = 0

∴  The required quadratic equation is x² + 2x – 35 = 0