Find quadratic polynomial whose zeroes are :

Let the zeroes of the quadratic polynomial be

α = 1 + 2√3, β = 1 – 2√3

Then, α + β = 1 + 2√3 + 1 – 2√3 = 2

αβ = (1 + 2√3) × (1 – 2√3) = 1 – 12 = – 11

Sum of zeroes = α + β = 2

Product of zeroes = αβ = – 11

Then, the quadratic polynomial

= x² – (sum of zeroes)x + product of zeroes

= x² – (2)x + ( – 11)

= x² – 2x – 11