F4 A-MATHS [ INEQUALITIES' ]

We consider "△<0" because "△<0" can imply the expression "x^2-mx+(m+3)" must be > 0. Let's consider the meaning of the range of △.

1. △ > 0: Equation has 2 real roots
If x^2-mx+(m+3) = 0, there will be 2 answers of real number x.
2. △ = 0: Equation has 1 real root / a double real root
If x^2-mx+(m+3) = 0, there will be only 1 answer of real number x.
3. △ < 0: Equation has no real root
If x^2-mx+(m+3) = 0, there will be no answer of real number x, that is, you cannot find any real number x such that x^2-mx+(m+3) = 0.

Now, x^2-mx+(m+3) is always positive for all real values of x, that is x^2-mx+(m+3) > 0 for all real number x. This mean, it is not possible to find any real number x such that x^2-mx+(m+3) = 0. △ < 0 can logically represent this condition.

As follows~~~


圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/inequality2.jpg?t=1190383884