Hi, everyone..I'm a new recruit and just joined this forum several weeks ago. So, hope u all can help me through every difficulties I face..yeah, this is my first ever question and I hope there's somebody can help me out...I'm not sure its the question problems or its mine problems..anyways have a look, thanks..
a) Find the set of values of m for which the graph of y = (3 - m)x^2 + 4x - m lies above the x-axis for all real values of x.
Hello, Ah Chan!
First of all, the parabola must open upward.Find the set of values of for which the graph of .
lies above the -axis for all real values of
. . Hence, the leading coefficient must be positive: . .
Second, there are no -intercepts.
. . That is, the equation: . . has no real roots.
Quadratic Formula: .
To have no real roots, the discriminant must be negative: .
There are two cases: .
. which contradicts .
. which agrees with .
. . . . Therefore: .