Question

How can you find the zeros of x^5-3x^4-24x^3-72x^2-25x+75=0, since it cannot be factored?

Answer 1

\[x^5-3x^4-24x^3-72x^2-25x+75=0\]

Answer 2

@SolomonZelman

Answer 3

Are you sure, it is not +72x² ?

Answer 4

yup

Answer 5

could be a typo in the question but that is what it says

Answer 6

well, for +72,
\(\normalsize\color{black}{ x^5-3x^4-24x^3+72x^2-25x+75=0\huge\color{white}{ \rm │ }}\)
\(\normalsize\color{black}{ x^4(x-3)-24x^2(x-3)-5(x-3)=0\huge\color{white}{ \rm │ }}\)
\(\normalsize\color{black}{ (x^4-24x^2-5)(x-3)=0\huge\color{white}{ \rm │ }}\)
and then you get `x-3` as the obvious part, and the first factor with completing the square....

Answer 7

I don't know how to do it, with -72x²... sorry _:(

Answer 8

OK, thanks anyways.

Answer 9

@ganeshie8 @DangerousJesse

Answer 10

I didn't help much -:(

Answer 11

It's fine

Answer 12

wolfram

Answer 13

Yep

Answer 14

I always use wolfram to graph

Answer 15

Thats how I though you could do it but there are also 2 complex solutions

Answer 16

*is

Answer 17

I am really thinking it should be +72x²

Answer 18

no, are

Answer 19

Then it is much better and easier.

Answer 20

yes there `are` also 2 complex solutions.

Answer 21

Complex solutions are fairly quick to find, have you already found the two?

Answer 22

http://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php

Answer 23

I'm not sure on how to find the complex solutions

Answer 24

\[x = \sqrt of x^5-3 x^4-24 x^3-72 x^2-25 x+75 \approx x = -1.84865-2.1615 i\]

Answer 25

there are approximated just like on wolfram.

Answer 26

You can use `~` for space.

Answer 27

If you put ~~ it will give more space, and ~~~ even more space, and on...

Answer 28

These are the exact complex solutions

Answer 29

\[x = \sqrt of x^5-3 x^4-24 x^3-72 x^2-25 x+75 \approx x = -1.84865+2.1615 i\]

Answer 30

OK, so use the graphing software to get the real solutions, and use that method to get the complex ones.

Answer 31

Yeah, I'd do that if I were you.

Answer 32

OK, thanks, again :P

Answer 33

No problem.