Accepted Answer

Hi, i think that the following examples can be useful:

First of all: the equation in gral is ax^2+bx+c=0

And the discriminant of the eqaution is b^2-4ac

There are 3 cases:

1) b^2-4ac > 0 then the equation ax^2+bx+c=0 has two real distinct solutions

Example: x^2-5x+6=0 (equation) where a=1,b=-5,c=6
then discriminant = (-5)^2-4(1)(6)=25-24=1>0 then the equation
x^2-5x+6=0 has two real distinct solutions


2) b^2-4ac = 0 then the equation ax^2+bx+c=0 has only one real solution
Example: x^2-2x+1=0 a=1,b=-2,c=1
discriminant is (-2)^2-4(1)(1)=4-4=0
then the equation x^2-2x+1=0 has only one real solution

3) b^2-4ac < 0 then the equation ax^2+bx+c=0 has no real solution

Example: x^2+x+1, a=1,b=1,c=1
discriminant= 1^2-4(1)(1)=-3<0
then the equation x^2+x+1 has no real solutions


Please ask me if you have any doubt

Any bonus is appreciated

Thanks

Steve

Expert:	Steve
Pos. Feedback:	100.0 %
Accepts:	1167
Answered:	1/19/2009

Teacher

I teach Calculus and Probability in an University since 1994