03 Nov 08
2 edits
I have this math problem that I am stuck on. You have to find f(x) if the roots are x=(1/7), -6+3i, -6-3i, ((-5+sqrt(7))/(2)), and ((-5-sqrt(7))/(2)), and the y-intercept is (0,-162) and f(-5) does not exist. You also have to find the oblique asymptote and explain why f(-5) does not not exist. I think that I found the correct function: f(x)=5.6x^5-40x^4-53.2x^3+966x^2+997.2x-162, but I don't know how to find the oblique asymptote, or why f(-5) does not exist. I have probably been very confusing in wording this problem, but I did the best I could. Would any of you guys happen to know how to find the oblique asymptote or why f(-5) does not exist? Any help would be greatly appreciated.
03 Nov 08
Originally posted by UserChevyWithout specifying some other attributes of f, there are uncountably many answers.
I have this math problem that I am stuck on. You have to find f(x) if the roots are x=(1/7), -6+3i, -6-3i, ((-5+sqrt(7))/(2)), and ((-5-sqrt(7))/(2)), and the y-intercept is (0,-162) and f(-5) does not exist. You also have to find the oblique asymptote and explain why f(-5) does not not exist. I think that I found the correct function: f(x)=5.6x^5-40 ...[text shortened]... find the oblique asymptote or why f(-5) does not exist? Any help would be greatly appreciated.
03 Nov 08
Originally posted by UserChevyi think the equation you are looking for can be found from a few steps:
I have this math problem that I am stuck on. You have to find f(x) if the roots are x=(1/7), -6+3i, -6-3i, ((-5+sqrt(7))/(2)), and ((-5-sqrt(7))/(2)), and the y-intercept is (0,-162) and f(-5) does not exist. You also have to find the oblique asymptote and explain why f(-5) does not not exist. I think that I found the correct function: f(x)=5.6x^5-40 ...[text shortened]... find the oblique asymptote or why f(-5) does not exist? Any help would be greatly appreciated.
1. let the product of all the roots = g(x) (ex. (7x-1)(x^2+6x+15)(4x^2+20x+18) = g(x) )
in other words, let each of the roots = zero, rearrange to put all the terms on one side (i.e. x=1/7 becomes 7x-1=0) and then using the reverse of the zero-product rule, you can find a polynomial that gives you zero.
now, for this equation, g(0) = -270 which is not -162. so you have to multiply through by a constant multiplier, in this case let f(x) = 162/270 * g(x). now we have the first two parts in order.
for f(-5) not to exist, the denominator must -> 0 as x->-5, in other words, put an (x+5) in the denominator.
and as far as an oblique asymptote goes, there are a number of possible answers. if there is only an (x+5)^1 power in the denominator, then there's no asymptote so the function rises to infinity. if there is a higher degree (for example (x+5)^15 ) in the denominator, then as x moves toward positive infinity, a horizontal asymptote of y=0 appears.
however, if the degree in the numerator is one greater than the degree of the denominator (our roots give us a 5th degree polynomial beginning with 28x^5) an oblique asymptote will be apparent as x approaches infinity. so... let the denominator be (x+5)^4, and do a little polynomial division. you will get a linear term and a fraction that goes to zero. so the oblique asymptote will be y = (linear term of the division)
i hope this helps i'm just too lazy to do the actual work for the last part and hopefully you'll know follow what i'm trying to say
03 Nov 08
Originally posted by AetheraelAm I nerdy to like this posting? I loved it!
i think the equation you are looking for can be found from a few steps:
1. let the product of all the roots = g(x) (ex. (7x-1)(x^2+6x+15)(4x^2+20x+18) = g(x) )
in other words, let each of the roots = zero, rearrange to put all the terms on one side (i.e. x=1/7 becomes 7x-1=0) and then using the reverse of the zero-product rule, you can find a polyno ...[text shortened]... do the actual work for the last part and hopefully you'll know follow what i'm trying to say
04 Nov 08
1 edit
Originally posted by AetheraelThis was a very helpful post, thanks for helping out. I still think that I might have messed up the oblique asymptote, as I got a 5th degree polynomial for the oblique asymptote, but it is supposed to be a 4th degree polynomial? Oh well, I think that I got the right function anyways, and thank you for your post.
i think the equation you are looking for can be found from a few steps:
1. let the product of all the roots = g(x) (ex. (7x-1)(x^2+6x+15)(4x^2+20x+18) = g(x) )
in other words, let each of the roots = zero, rearrange to put all the terms on one side (i.e. x=1/7 becomes 7x-1=0) and then using the reverse of the zero-product rule, you can find a polyno do the actual work for the last part and hopefully you'll know follow what i'm trying to say