How do you write a polynomial with zeros 2, $4 + \sqrt{5}$ $4+sqrt5$ , $4 - \sqrt{5}$ $4-sqrt5$ ?

Question

1415 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-07T17:52:33

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

The polinonimal will be the result of

$(x - 2) (x - 4 - \sqrt{5}) (x - 4 + \sqrt{5})$ $(x-2)(x-4-sqrt(5))(x-4+sqrt(5))$

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

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

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

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

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

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

How do you write a polynomial with zeros 2,4+√5 4+sqrt5, 4−√5 4-sqrt5?