My instructor told us, to solve a quadratic inequality factor out it's roots to set up a test interval on a number line. Then, test to see at what positions the inequality is true.

My question:

Descartes rule of signs:

0 positive roots

1 negative root

rational root theorem:

Synthetic division:

............-4..0

-4......1..4..4..

........1..0..4----

not a root

............-2..-4

-2.......1..4..4

.........1..2..0--------

a root!

root=-2

But, this is a double root.

And because it is a double root my interval is... not applicable besides

But my textbook says the answer is:

Any help on this problem?

Also, if anyone has a more 'algebraic' way of solving a quadratic inequality, please post it. I hate guess and check problems.