Posted by kaley on Thursday, March 1, 2012 at 10:27pm.
find all the zeros of the polynomial function
F(x)= x^4+4x^36x^236x27

Algebra 2  drwls, Thursday, March 1, 2012 at 11:02pm
There are websites that solve such rootfinding questions automatically, but they are not very instructive.
If there are integer roots, they must be even divisors of 27: +/ 1, 3, 9 or 27.
That is a consequence of the "rational roots theorem", which you should learn.
One such root is 1, so x+1 is a factor.
The other factor is
(x^4+4x^36x^236x27)/(x+1)
= x^3 +3x^2 9x 27
(obtained with polynomial long division)
x = 3 is clearly another root, so (x3) is another factor. Divide the cubic by (x3) and you get
x^2 + 6x +9 = 0
which can be factored to give
(x+3)^2 = 0
That means x = 3 is a double root.
The roots are 3, +3 and 1
Answer This Question
Related Questions
 algebra  Using the rational zeros theorem to find all zeros of a polynomial The...
 algebra  Using the rational zeros theorem to find all zeros of a polynomial The...
 Algebra  Can someone please explain how to do these problems. 1)write a ...
 algebra  p(x)=x^3+2x^23x+20 one of this functions zeros is 4 When using ...
 college algebra  use the rational zeros theorem to find all the real zeros of ...
 College Algebra  Use the rational zeros theorem to find all the real zeros of ...
 Polynomiials  Find a polynomial function with real coefficients that has the ...
 algebra  Use the rational zeros theorem to find all the real zeros of the ...
 Algebra  Use the rational zeros theorem to list the potential reational zeros ...
 College algebra  Use the rational zeros theorem to find all the real zeros of ...
More Related Questions