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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?
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.
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.........
Need further help????? Please sign up to our site
www.learningscholars.com
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.........
Need further help????? Please sign up to our site
www.learningscholars.com
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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
(x^2-6)(X^2+1)=0
X^2=-1, which is not possible so sqrt6 is the only solution