(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
