how do I find the zeros of x^4 - x^3 -2x^2 algebraically?

Question

anonymous · Answer

well that's what got

e.mccormick · Answer

You can factor it or use assorted tests to find possible ones and test them with division. Those are two possible ways.

anonymous · Answer

my book says x= -1, 0, 0, 2

e.mccormick · Answer

The 0 should be obvious because all terms have x in them.

e.mccormick · Answer

$ x^4 - x^3 -2x^2 \implies $

$x^2( x^2 - x -2)  $

See, the $x^2$ out front makes for the 0 parts of your answer.  Then you just need to factor the part in the ( ) to get the others.

When something says to find the roots, factors, zeros, x intercepts, or solutions for = 0, they are all asking for the same thing.

anonymous · Answer

thankyou

e.mccormick · Answer

Do you understand the rest of how to do these?

e.mccormick · Answer

This is an example and NOT your problem:

Lets say I had the factored form of $(x-5)(x+3)x$.  Then the roots/zeros are when that = 0.

$(x-5)(x+3)x=0$ means:

$x-5=0$ or
$x+3=0$ or
$x=0$

So by solving each of those factors for x, I know the roots/zeros.

$x-5+5=0+5$ or
$x+3-3=0-3$ or
$x=0$

$x=5$ or
$x=-3$ or
$x=0$

So the roots/zeros are at $x=-3,0,5$

Well, what if I was given:
$x^3-2x^2-15x$

It would be the same.  See, that is just the non-factored form of the same thing.  That is why factoring these really helps.  That is why I started by factoring yours.