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```        Sir
Here is my question,
Q. If p and  q are the roots of the equation ax2+bx+c=0 & r and -q are the roots of lx2+mx+n=0,then show that p and r are the roots of  (b/c+m/n)x2 + (b/a+m/l)(b/c+m/n)x + (b/a+m/l) = 0
Hope to get an answer soon.```
10 years ago

```							p+q=-b/a              pq=c/a
r-q=-m/l                -qr=n/l
Let p,r be roots of
tx2+vx+w=0
then p+r = -v/t
and pr=w/t
As you know, p+r = -b/a - m/l
pr = ?
Now Solve these two equations for q2:
aq2+bq+c=0-------------------X m ................1
lq2-mq+n=0...................X b.................2

q2 = - [mc+nb]/[am+lb]
-prq2= cn/al
Hence find out
pr = [m/l + b/a]/[m/n+b/c]=
p+r = -[b/a + m/l]
Also
p+r = -v/t
pr=w/t

Subtitue values for
w/t = [m/l + b/a]/[m/n+b/c]
and
-v/t = -[b/a + m/l]
And finally you'll get the required equation.

```
10 years ago
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