2x^4-x^2-6x+14=0
2006-09-03 07:02:45 · 7 answers · asked by Th_hT 1 in Science & Mathematics ➔ Mathematics
First, let's look for a linear factor.
If a/b is a rational root of this equation,
then a divides 14 and b divides 2.
If this fails, let's see if the left hand side is
the product of 2 quadratic factors.
Write
2x^4-x^2-6x+14 as (ax^2 + bx + c)(dx^2 + ex + f).
Multiply out the right-hand side and equate like
powers of x and see if you can find a solution.
If this fails, then the left-hand side is irreducible.
I couldn't get any of these to work, so I went to PARI
(an algebraic calculator) and it verified that
the left-hand side of this equation is indeed irreducible.
2006-09-04 06:48:53 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
x(2x^3-x-6)+14=0
2006-09-03 22:12:06 · answer #2 · answered by jas_chloe16 1 · 0⤊ 1⤋
There are no real roots of this equation.
so, as one solution given in the first answer, you can make many more similar simplifications depending on what u want to do next !
2006-09-03 14:23:36 · answer #3 · answered by DG 3 · 0⤊ 0⤋
It's not factorable becuase it doesn't hit the x-axis so there are no real solutions so therefore it is not factorable.
2006-09-03 14:33:49 · answer #4 · answered by Anonymous · 0⤊ 0⤋
2x(x^2-1)-2(3x+7)=0
2006-09-03 14:09:09 · answer #5 · answered by Kim :) 2 · 0⤊ 2⤋
http://i4.photobucket.com/albums/y147/nixie_zh/function.jpg
This diagram shows that it does not intersect x-axis, and is therefore not factorable.
2006-09-03 14:43:24 · answer #6 · answered by Hex 2 · 0⤊ 0⤋
that is hard
2006-09-03 14:18:09 · answer #7 · answered by Kyrsten 2 · 0⤊ 0⤋