range of values for m?

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

range of values for m?

Postby hadimotamedi » Mon Aug 01, 2011 11:54 pm

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?

Postby blitzer6266 » Tue Aug 02, 2011 11:29 pm

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

This should lead you to the right answer

DDswife
Posts: 149
Joined: Thu Aug 14, 2014 5:29 pm

Re: range of values for m?

Postby DDswife » Sun Aug 24, 2014 4:54 pm

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: 149
Joined: Thu Aug 14, 2014 5:29 pm

Re: range of values for m?

Postby DDswife » Tue Aug 26, 2014 9:55 pm

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




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