How do you find all the zeros of $x^{5} + x^{3} - 30 x$ $x^5+x^3-30x$ ?

Question

How do you find all the zeros of $x^{5} + x^{3} - 30 x$ $x^5+x^3-30x$ ?

1 Answer

Impact of this question

3174 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-08T21:55:44

Factor to find zeros:

$0, \pm \sqrt{5}$ $0, +-sqrt(5)$ and $\pm \sqrt{6} i$ $+-sqrt(6)i$

Explanation:

After separating out the common factor $x$ $x$ , the remaining quartic can be factored like a quadratic, before reducing to linear factors:

$x^{5} + x^{3} - 30 x = x (x^{4} + x^{2} - 30)$ $x^5+x^3-30x = x(x^4+x^2-30)$

$x^{5} + x^{3} - 30 x = x (x^{2} + 6) (x^{2} - 5)$ $color(white)(x^5+x^3-30x) = x(x^2+6)(x^2-5)$

$x^{5} + x^{3} - 30 x = x (x - \sqrt{6} i) (x + \sqrt{6} i) (x - \sqrt{5}) (x + \sqrt{5})$ $color(white)(x^5+x^3-30x) = x(x-sqrt(6)i)(x+sqrt(6)i)(x-sqrt(5))(x+sqrt(5))$

Hence zeros:

$0, \pm \sqrt{5}$ $0, +-sqrt(5)$ and $\pm \sqrt{6} i$ $+-sqrt(6)i$

Science

Math

Humanities

... and beyond

How do you find all the zeros of $x^{5} + x^{3} - 30 x$ $x^5+x^3-30x$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find all the zeros of x5+x3−30xx^5+x^3-30x ?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find all the zeros of $x^{5} + x^{3} - 30 x$ $x^5+x^3-30x$ ?