Question

Help me pls!!!

Answer 1

let the roots of
\[ax ^{2} + 2bx + c =0\] be \[\alpha\ and\ \beta\]
and
the roots of
\[px ^{2} + 2qx + r = 0\]
be
\[\gamma \ and \ \delta \]

Answer 2

if the roots
\[\alpha,\beta,\gamma,\delta \] r four successive terms of a geometric progression
then prove...
\[\frac{ ac }{ b ^{2} }=\frac{ pr }{ q ^{2} }\]

Answer 3

pls help @goformit100 @ganeshie8 , @robtobey ,

Answer 4

@thomaster , @texaschic101 , @Zarkon , @ajprincess @SWAG help me pls!!

Answer 5

The four roots are:
{-b - (b^2 - ac)^1/2}/a, {-b + (b^2 -ac)^1/2}/a,
{-q - (q^2 - pr)^1/2}/p, {-q + (q^2 - pr)^1/2}/p
They are in geometric progression. So the second term divided by first term = the fourth term divided by third term. Cross multiply and simplify.

Answer 6

Thanks... but the question has to be proved without using finding the roots of 2 quadratic expression
i.e
all the data u can get is
\[\alpha + \beta = \frac{ -2b }{ a }\]\[\alpha \beta = \frac{ c }{ a }\]\[\gamma + \delta =\frac{ -2q }{p}\]\[\gamma \delta = \frac{ r }{p }\]

that's y I'm stuck on this one!!!

Answer 7

Any idea ..how to get that answer with these ?

Answer 8

I am new here and I have not figured out how to use the mathematical symbols and alpha, beta, etc. But alpha, beta, gamma, delta are in geometric progression. So beta = alpha times r and delta = gamma times r. Substitute in your 4 equations above.

Answer 9

Sorry .. I didn't get wt u just tell could u pls show me an example substitution u 've mentioned?

Answer 10

ranga means this think :-

say, the four roots are

\(\large \alpha, m\alpha, m^2\alpha, m^3\alpha\)

Answer 11

\(m\) is the common ratio n of GP

Answer 12

Since they are Geometric progression, beta = alpha x r and delta = gamma x r
Take the first two equations and replace beta with (alpha x r). Solve for r (without any alpha in the solution).
Take the last two equations and replace delta with (gamma x r). Solve for r (without any gamma in the solution).
Equate the two solutions for r.

Answer 13

could u explain how did u get those equations ?

Answer 14

then, from ur 4 equations we wud have :-

\(\large \alpha (1+ m ) = \frac{-2b}{a}\) --------(1)

\(\large m \alpha^2 = \frac{c}{a}\) ----------(2)


\(\large m^2 \alpha(1+m) = \frac{-2q}{p}\) -------(3)

\(\large m^5\alpha^2 = \frac{r}{p}\) --------(4)

Answer 15

i just did SUM of roots, and PRODUCT of roots, as u did before

Answer 16

Sorry 'r' is already in the problem. So use 'm' as the factor in geometrci progression.

Answer 17

thanks! I understand it so far... So.... whats next ?

Answer 18

next is weesy,

we do below two :-

(3) / 1

(4) / 2

Answer 19

u should see the final result...

Answer 20

??

Answer 21

THANKS U SOOOOOO MUCH GUYS!!! It really have gone off road from the methods I've learn.... But I got figured it out how to do it 'cause of u guys and I don't have words to thank u ... I really want to give medals to both of u !! But I can only give one ... How sad

Answer 22

lol np :)
may be we can share among ourselves i gave it to ranga, ranga can give u.. u deserve too... as u started approaching the problem correctly :)

Answer 23

Oh, thanks! @ganeshie8