Just need some help remembering how to do this. finding exact roots of y=X^3+2x^2-7x+4 without using a calculator. It says try synthetic division or factoring, but I forgot how to group.

Question

amistre64 · Answer

x^3 +2x^2 -7x +4

grouping doesnt look easy

amistre64 · Answer

use the rational roots thing; +-(1,2,4)

amistre64 · Answer

(1)^3 +2(1)^2 -7(1) +4

1 +2 -7 +4 = 0; so (x-1) is a root

amistre64 · Answer

if we synthd it we could have seen the other part :)

amistre64 · Answer

1  2  -7  4 
    0  1   3 -4
   ---------
1 | 1 3 -4  0

(x-1) (x^2 +3x -4)

amistre64 · Answer

the quad is easy enough now

anonymous · Answer

Can you remind me of the "rational roots thing"? I vaguely remember my teacher saying something like "Factors of the first/factors of last"

amistre64 · Answer

yep; thats it.  ideally, the results of any of your factors will result in the first and last coeffs over all; so those are the important ones

amistre64 · Answer

ax^2 + bx + c  ; divide of that "a"
/a         /a    /a
---------------
x^2 +bx/a + c/a

amistre64 · Answer

factors of c/a are what you need

amistre64 · Answer

last
---
first

amistre64 · Answer

if you cant find them in there; then its gonna be irrational roots and those i aint got a clue about :)

anonymous · Answer

Alright thank you very much, so according to the math the roots of this cubic would be at (X-1)(X-1)(X+4). So (1,0) and (-4,0)?

amistre64 · Answer

yep

anonymous · Answer

Thank you very much for your time Amistre64!