Quadratic polynomial

Question

Find the quadratic polynomial whose zeroes are √2+1, 1/√2+1

Answer 1

If you have 2 zeros x₁ and x₂, then any function of the form

 

f(x) = A(x - x₁)(x - x₂),

 

with A ≠ 0, answers this question.  You have the 2 zeros.  Plug them into f(x), pick any real nonzero value for A, and expand into the standard form of a quadratic polynomial.