How do you write a polynomial with zeros 2, $4+sqrt5$ , $4-sqrt5$ ?

Question

1427 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-07T17:52:33

$x^3-10x^2+27x-22$

The polinonimal will be the result of

$(x-2)(x-4-sqrt(5))(x-4+sqrt(5))$

$(x-2)((x-4)^2-5)$

$(x-2)(x^2-8x+16-5)$

$(x-2)(x^2-8x+11)$

$x^3-8x^2+11x-2x^2+16x-22$

$x^3-10x^2+27x-22$ or a multiple of it:

$a(x^3-10x^2+27x-22)$

How do you write a polynomial with zeros 2, 4+sqrt5 4+sqrt5, 4-sqrt5 4-sqrt5?