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gopal nair Grade: 12
        

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.

7 years ago

Answers : (1)

Askiitian.Expert Rajat
24 Points
										

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.


 


 

7 years ago
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