Dear All
For what values of m, the following curve will pass from all of the four quadrants of the xyplane?
y=(m+2)x^22x+1
range of values for m?

 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)
This should lead you to the right answer
This should lead you to the right answer
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
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
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