Find quadratic polynomial whose zeroes are :

Let the zeroes of the quadratic polynomial be

Then,

Sum of zeroes = α + β = 2

Product of zeroes = =

Then, the quadratic polynomial

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

=

=

=

We can consider 4x² – 8x – 1 as required quadratic polynomial because it will also satisfy the given conditions.