Let α = 2 and β = - 6
Sum of the zeroes, (α+ β) = 2 + (- 6) = - 4
Product of the zeroes,αβ = 2 × (-6) = -12
∴ Required polynomial = x2 - (α +β)x + αβ = x2 – (- 4)x – 12
= x2 + 4x – 12
Sum of the zeroes = -4 = \(\frac{-4}1\) = \(\frac{-(coefficient\,of\,x)}{(coefficient\,of\,x^2)}\)
Product of zeroes = -12 = = \(\frac{-12}1\) = \(\frac{constant\,term}{(coefficient\,of\,x^2)}\)