## range of values for m?

Forum for the GRE subject test in mathematics.
Posts: 34
Joined: Thu Dec 30, 2010 4:36 am

### range of values for m?

Dear All
For what values of m, the following curve will pass from all of the four quadrants of the xy-plane?
y=(m+2)x^2-2x+1

blitzer6266
Posts: 61
Joined: Sun Apr 04, 2010 1:08 pm

### Re: range of values for m?

Hint: A parabola will hit all quadrants iff it has a positive and negative root (picture is a good enough proof)

DDswife
Posts: 154
Joined: Thu Aug 14, 2014 5:29 pm

### Re: range of values for m?

Hint 2: a quadratic equation whose leading coefficient doesn't necessarily have to be one. The first coefficient might be 0. In this case, it won't be in the 4 quadrants

To check of the roots have different signs, their product should be negative. And the products of the roots of ax^2+bx+c = 0 is c/a

DDswife
Posts: 154
Joined: Thu Aug 14, 2014 5:29 pm

### Re: range of values for m?

Hint 3. y(0) =1. So, it will only have a positive and a negative zeros if the leading coefficient is negative