Question

If the roots of the equation a(x)^2 + bx + c = 0, are in the ratio m:n, prove that:
mn . (b)^2 = ac (m+n)^2

Answer 1

I did it in the following way. Is it correct?

Answer 2

Let p,q be the roots.
We know that, p + q = -(b/a)
And, pq = c/a
Given , p/q = m/n
So, LHS = mn. b. b = b^2 . c/a

Now, RHS = ac (m+n)(m+n) =ac. [(-b)/a]^2 = b^2.c/a
So, LHS = RHS proved.

Is it correct?

Answer 3

That looks correct to me.

Answer 4

Really? I want to get it confirmed from others also.

Answer 5

The only thing that wasn't immediately clear to me, was why mn=c/a, and why m+n=(-b/a). If you explained that more clearly, I would be an excellent proof.

Answer 6

See, I have taken, p/q = m/n
We know that, in a quadratic equation, sum of the roots = -b/a
Product of roots = c/a

Answer 7

It's the substitutions you were doing for m and n that I didn't immediately see. Like I said, if you elaborated on that part of the proof, it would be an excellent proof.

Answer 8

Okay. Vishal Bhai, is it correct? Its a 4 mark question.

Answer 9

let me see it properly...

Answer 10

Yeah.

Answer 11

oh no light gayi....but i can tell use the quadratic formula....

Answer 12

I didn't understand.

Answer 13

truly speaking india needs development....