Question

If A,B are the roots of px^2+px+r=0, form an equation whose roots are (2A+1/A), (AB+1/B)
.
.
Answer= prx^2+q(2r+p)x+(2r-p)^2+2q^2

Answer 1

Formula for forming the equation
x^2-(sum of roots)x+(product of roots)=0

Answer 2

I am stuck at product of roots

Answer 3

sum=-q/p
product=r/p

Answer 4

Sum of given roots:
(2A+1/A)+(2B+1/B)

Answer 5

\[(2A+2B) +(\frac{ 1 }{ A }+\frac{ 1 }{ B })\]

Answer 6

I got the sum of roots which was
\[\frac{ -q(2r+p) }{ pr }\]

Answer 7

having problem in product of roots

Answer 8

(2A+1/A)*(2B+1/B)

Answer 9

anyone there?

Answer 10

its been an hour since I asked the question and got no answer yet :/

Answer 11

(2A+1/A)*(2B+1/B)
what u get after multiplying them out ?

Answer 12

oh finally someone came to my Q

Answer 13

:D

Answer 14

I am showing step by step what I did

Answer 15

4AB + 2A/B +2B/A +1/AB

Answer 16

so, u only have problem with 2A/B +2B/A part, right ?

Answer 17

YUP

Answer 18

problem in simplification of product of roots

Answer 19

(4AB + 1/AB) + (2A/B + 2B/A)

Answer 20

so, 2 [A^2+B^2]/AB
so you just need, A^2+B^2, right ?

Answer 21

(4AB^2+1 / AB ) + ( 2A^2+2B^2/AB)

Answer 22

note that you already know AB =....

Answer 23

so, you know (4AB + 1/AB)

Answer 24

yes and A+B too

Answer 25

so, finally , you just need A62+B62, right ?

Answer 26

A^2+B^2

Answer 27

\[\frac{ 4(\frac{ r }{ p })^2+1 }{ \frac{ r }{ p } }\]

Answer 28

yes it will expand by formula..right?

Answer 29

(4A^2+4B^2)-8AB

Answer 30

huh ? what ?

Answer 31

(4AB + 1/AB) + (2A/B + 2B/A)
= 4 (r/p) + p/r +(2A/B + 2B/A)
right ?

Answer 32

\[2A+\frac{ 1 }{ A } * 2B+\frac{ 1 }{ B }\]

Answer 33

don't miss the brackets.....
are u clear till here ?
(4AB + 1/AB) + (2A/B + 2B/A)
= 4 (r/p) + p/r +(2A/B + 2B/A)

Answer 34

AB = r/p
so, 1/AB = p/r

Answer 35

OK

Answer 36

now you need (2A/B + 2B/A)
= 2 [A^2+B^2]/AB
right ?

Answer 37

OKAY

Answer 38

now use the fact that A^2+B^2 = (A+B)^2 - 2AB
you know both A+B and AB

Answer 39

A^2+B^2 WILL EXPAND BY FORMULA??

Answer 40

OK .OK

Answer 41

try it, if you don't get it now, then tell me.

Answer 42

I SIMPLIFIED IT

Answer 43

and got it till \[\frac{ 4r^2+p^2+2q^2-2rp }{ pr }\]

Answer 44

px^2+px+r=0
where is the q ? i didnt see it :P

Answer 45

i assumed px^2+qx+r=0

Answer 46

sorry @RadEn TYPING PROBLEM

Answer 47

I DID IT (2r-p)^2+2q^2/pr

Answer 48

*applauses*