anonymous
  • anonymous
what are the roots of i) f(x)=X^4-6x^3+10x^2+2x-15 ii) f(x)=x^3+11x^2+ 31x+21
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
try synthetic division
anonymous
  • anonymous
You should try to find roots according to the rational toot theorem. If you can find rational roots, you can then divide these factors out to simplify the polynomial. The aim is to find a couple of factors in the first one you can use to diminish the degree of the quartic to 2. The rational root theorem gives -1 and 3 as possibilities here for the first polynomial (technically, +/1{1,3,5,15}, but -1 and 3 will work).
anonymous
  • anonymous
*+/-*

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
You can use the theorem again for the second. The theorem says, if you have a polynomial \[P(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0\]then if P has rational roots, they will be of the form,\[x=\frac{p}{q}\]where p and q are coprime in Z and where the numerator is an integer factor of the constant term \[a_0\]and the denominator is an integer factor of \[a_n\].
anonymous
  • anonymous
If you exhaust all combinations of this form, your polynomial has no rational roots.
anonymous
  • anonymous
The possible factors to consider in the numerator for the second equation are the factors of 21 (last term) +/-{1,3,7,21} The possible factors to consider for your denominator are +/-{1} (the coefficient of your highest term is 1) So you consider all possible combinations of \[\frac{p}{q}\]where p is from the first list and q is from the second.
anonymous
  • anonymous
Here, for the second, if you try -1, -3 and -7, you'll find each is a root.
anonymous
  • anonymous
^ second equation, I mean.
anonymous
  • anonymous
hi
anonymous
  • anonymous
hi

Looking for something else?

Not the answer you are looking for? Search for more explanations.