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elitewarr
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Homework Statement
2) Given a cubic equation y = (x+5)(ax^2 + bx - 2). Give conditions on a and b for the equation to represent the following curve. The curve is attached to the email.
http://img35.imageshack.us/img35/8246/question2o.png
Homework Equations
The Attempt at a Solution
I know that a>0.
Since there are 3 intersections with the x-axis, then for (ax^2 + bx - 2), b^2 - 4ac > 0.
b^2 - 4(a)(-2) > 0
b^2 + 8a > 0
b^2 > -8a
If i differentiate it, I get
3ax^2 + 2bx + 10ax + 5b - 2
Since there are 2 stationary points,
B^2 - 4ac = (2b + 10a)^2 - 4(3a)(5b-2) > 0
b^2 - 5ab + 25a^2 + 6a > 0
and I'm stucked again.
Which approach is correct?
Thanks.
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