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

Are the zeros meant to be $-1,1,\sqrt2$ or $1,1,\sqrt2$? – lhf Dec 18 '17 at 18:43 — lhf, Dec 18 '17 at 18:43

score 2 · Answer 1 · answered Dec 18 '17 at 18:36

2

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

answered Dec 18 '17 at 18:36

lhf

216,483

I assume the OP meant zeros to be $1$ (twice) and $\sqrt 2$. – lhf Dec 18 '17 at 18:44

score 1 · Answer 2 · answered Dec 18 '17 at 18:38

1

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

answered Dec 18 '17 at 18:38

A. Goodier

10,964

1

@lhf $3(-2)(-1)=6$, so $3$ is fine. – Botond Dec 18 '17 at 18:41

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

2 Answers2