Let ∝ = 2/3 and β = -1/4
Sum of the zeroes = (∝ + β) = 2/3 + -1/4 = 5/12
Product of the zeroes, = 2/3 x -1/4 = -1/6
Required quadratic polynomial is
x2 – (∝+β)x + ∝β
= x2 – (5/12)x – (-1/6)
= 1/12(12x2 – 5x – 2)
And,
Sum of the zeroes = 5/12 = (-Coefficient of x)/(Cofficient of x2)
Product of zeroes = -1/6 = Constant term / Coefficient of x2