1. ## [SOLVED] polynomial inequality

Can someone assist me with this? I'm supposed to find the range of valid answers

$x^2+2x-3 < 0$

typically I'd just factor the left to figure out the zeros to get my critical points, then check each area to find the valid ranges. However, I can't factor the equation...unless I'm mistaken, it's not factorable. How do I get the answer?

2. (x+3)(x-1)

3. Originally Posted by satis
Can someone assist me with this? I'm supposed to find the range of valid answers

$x^2+2x-3 < 0$

typically I'd just factor the left to figure out the zeros to get my critical points, then check each area to find the valid ranges. However, I can't factor the equation...unless I'm mistaken, it's not factorable. How do I get the answer?
$x^2+2x-3=(x+3)(x-1)$

In order for this to be < 0,
one factor must be positive and the other negative.

Hence, if x+3 is positive, x > -3.
x-1 remains negative until x=1.
Hence -3 < x < 1

Also if x+3 is negative, x < -3
There is no way this range of x allows x-1 to be positive however.

Therefore -3 < x < 1.

Or, the graph is a parabola with the minimum under the x axis.
Hence, it's negative between the roots.