general second degree equation

When y＝0, the general equation becomes

3x²＋6x＋c＝0　　(1)

As the two straight lines intercept on the x-axis, equation (1) has two coincident real roots. Therefore,

6²－4(3)c＝0　＝＞　c＝3

By the condition for the general equation to represent two straight line, we have

　　3(－28)3＋2(17/2)(6/2)(－h)－3(17/2)²－(－28)(6/2)²－3(－h)²＝0

＝＞　　－252－51h－867/4＋252－3h²＝0
＝＞　　4h²＋68h＋289＝0
＝＞　　(2h)²＋2．17(2h)＋17²＝0
＝＞　　(2h＋17)²＝0
＝＞　　h＝17/2＝8.5

2008-06-28 18:39:21 補充：
Correction for last line:

＝＞　　h＝－17/2＝－8.5

2008-06-30 01:29:42 補充：
The word "intercept" on line 3 was used wrongly. It should be changed to "intersect".

3x² - 2hxy - 28y² + 6x + 17y + c = 0

represents two straight lines
Let
(Ax+By+C)(Dx+Ey+F)=3x² - 2hxy - 28y² + 6x + 17y + c = 0

Compare
AD=3
BE=-28
AF+CD=6
BF+CE=17
CF=c
AE+BD=-2h

Sub y=0
(Ax+C)(Dx+F)=0
So x=-C/A=-F/D

Also (Ax+C)(Dx+F)=0 or ADx^2+(AF+CD)x+CF=0, there is only one repeated root

discriminent=0
36-12c=0
c=3

Then x=-1

Now C=A,F=D

We can rewrite the system of equations as
AD=3
BE=-28
BD+AE=17
AE+BD=-2h

So h=-17/2