find all the rational zeros of the polynomial. use the quadratic equation if necessary
p(x)=x 4 −7x 3 +14x 2 −3x−9

Question

find all the rational zeros of the polynomial. use the quadratic equation if necessary 
p(x)=x 4 −7x 3 +14x 2 −3x−9

anonymous · Answer

hello ?

agreene · Answer

3

anonymous · Answer

thats what i dont understand isnt there suppose to be 4 since the degree is 4

agreene · Answer

no i mean the answer is 3
it also happens to have 3 roots.

anonymous · Answer

what do u mean

agreene · Answer

x=3 is the only rational root.

anonymous · Answer

yea 
but isnt there suppose to be 4

anonymous · Answer

4 zeros

agreene · Answer

basically, it is happening because the last time it swings up, it does so without crossing the axis again. it happens sometimes.|dw:1330984886647:dw|

agreene · Answer

but, anyway... if you factor the equation, and solve it after that--it is clear that 3 is the only rational root.

it factors to (-3+x)^2 (-1-x+x^2)

anonymous · Answer

oh okay so how do i know when that happens so i can just move on to the next problem? so if you multiply all the equations will i end up with the original equation?

agreene · Answer

it's hard to know when that happens--it normally wont though. And yes, if you multiply out the factored version you get the original.

anonymous · Answer

like how am i suppose to put $$X^3-4x^2+2x+3 $$
in quadrtatic form

agreene · Answer

i haven't the slightest. I never have, and probably never will use the quadratic formula.

anonymous · Answer

because thats how im suppose to get the rest of the two zeros but i dont know how to put that in quadratic form

agreene · Answer

i find all my zeros by completing the square, it's how i was taught to do it... never really learned the quadratic formula, had a few teachers try--i didn't like it, so i'm afraid i cant really help you on how to use it.
the roots of x^3-4x^2+2x+3 are
3
1/2(1-sqrt(5))
1/2(1+sqrt(5))
though ;)