-2 and 11/2

(iv) -2 and  11/2

Sol. The roots of the quadratic equation are -2 and 11/2.

Let α  = -2 and β  = 11/2

∴  α  + β  = -2 + (11/2) = (- 4 +11)/2 = 7/2

and αβ  = - 2  × 11/2 = - 11

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 – (7/2)x + (–11) = 0

Multiplying the equation by 2 we get,

∴  2x² - 7x – 22 = 0

∴  The required quadratic equation is 2x² - 7x – 22 = 0