Can someone help me with the steps to this problem: x^4 - 5x -6 = 0
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Can someone help me with the steps to this problem: x^4 - 5x -6 = 0

[From: ] [author: ] [Date: 12-01-27] [Hit: ]
x = sqrt -1,The computer is telling me that sqrt 6 is correct, but sqrt -1 or i is incorrect. Help?-Uh, you left out an exponent.......
http://courses.webwork.maa.org:8080/wwtmp/equations/fa/ed896502501d4d3cf9cb2181613cb51.png
I've done the follow steps (this is for online homework) but it's telling me one of my answers is wrong.
Here's what I have:
x^4 - 5x -6 = 0
x^2 - 5x - 6 = 0
(x - 6) (x + 1) = 0

x^2 = 6
x = sqrt 6
x = sqrt -1, or i

The computer is telling me that sqrt 6 is correct, but sqrt -1 or i is incorrect. Help?

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Uh, you left out an exponent...that's the source of your difficulty. It should be:

x^4 - 5x^2 - 6 = 0

Now you can consider x^2 to be a variable u = x^2 and factor:

u^2 - 5u + 6 = (u - 6)(u + 1) = (x^2 - 6)(x^2 + 1) = 0
The first factor is a difference of squares, so:

(x - √6)(x + √6)(x² + 1) = 0

...has real solutions x=√6 and x=-√6. The final factor has no real solutions.

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x^4 - 5x -6 = 0

f(x) = x^4 - 5x -6

f(-1) = 1 + 5 -6 =0

(x+1) is a factor

(x^4 - 5x -6)/ (x+1)
(x^3-x^2+x-6)

g(x) = (x^3-x^2+x-6)
g(2) = 8-4+2-6 =0
(x-2) is a factor

and so on.........

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x^4-5x-6=0
(x^2-6)(X^2+1)=0
X^2=-1, which is not possible so sqrt6 is the only solution
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