IIT JEE , AIEEE Forum - Mathematics , Algebra

Nithy

hi!

please help me out.

if ax^2 + bx + c=0 & a1x^2 +b1x+c1=0 have a common root, and if a/a1 , b/b1, c/c1 are in AP. then a1, b1, c1 are in??

please give me hints only.

i guess first apply common root condition...

then???

b_srikalyan009

u get (b1)^2 = 4 a1 c1.
so u cant say they are in gp or anything

metal

Hey,

there is a bit of a problem in your question. You wrote

ax²+bx+c=0 and ax²+bx +c=0 have a common root-------of course they have, they are the same equation!!!!!!!!!!

And you never mentioned what a1, b1, c1 are, did you??????

CHECK the QUESTION, buddy!!!!!!!!

metal

I think, you wanted to write that ax²+bx+c=0 and a1x²+b1x +c1=0 have acommon root. Am I correct?????

metal

Considerring, that my assumption of the question is correct,

you can try solving it like this:-

Let the common root be m

The equations, will then hold true for x=m.

now put x=m

am²+bm+c=0

and a1m²+b1m +c1=0

Now, try finding the relation between a1, b1,c1 and a,b,c.

You will get another relation from the fact that a/a1, b/b1, c/c1 are in A.P.

Using these two relations , you will get the desired relation of a1, b1, c1.

O.K.?????????

rate me if I have been of any help to you.

metal

Srikalyan,

where are you getting (b1)² =4 a1 c1 from???

Note that the equation does not have two equal roots, but one root of one equation is equal to one root of the other...

Nithy

they are in gp. am i right???

b_srikalyan009

u will definately get b1^2 = a1 c1 .
metal simplify u'r equation and see it u'r sely.