Find a polynomial that satisfy the given given conditions.... Zeros - 1,1,2^1/2 integer coefficient and constant term 6...

Question

Find a polynomial that satisfy the given given conditions.... Zeros - 1,1,2^1/2 integer coefficient and constant term 6... My question is how do I make them integers... I tried multiplying by square root 2 but I also get square... Any hint would be helpful Thank you

Answer 1

Hint: Start with $(x-1)^2(x^2-2)$.

Answer 2

Consider $$3(x^2-2)(x^2-1).$$ .