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.

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

Add 1 and 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.