Question

I don't know how the heck i should prove it

Answer 1

what to prove????

Answer 2

If r be the ratio of the roots of the equation ax^2 + bx +c = 0
show that
\[\frac{ (r+1)^{2} }{ r }= \frac{ b ^{2} }{ ac }\]

Answer 3

@mathslover

Answer 4

i think i got it its easy

Answer 5

i got it

Answer 6

Yeah, you just need to put \(r = \cfrac{\alpha}{\beta}\)

Answer 7

And then :

\(\cfrac{\left (\cfrac \alpha \beta + 1 \right )^2 }{\cfrac{ \alpha }{\beta}}\)

\( = \cfrac{\cfrac{\left(\alpha + \beta \right )^2 }{\beta^2}}{\cfrac{\alpha}{\beta}}\)

= \(\cfrac{\left (\alpha + \beta \right )^2 }{\alpha \beta}\)

Since, sum of the roots = \(\cfrac{-b}{a}\)

and Product of Roots = \(\cfrac{c}{a}\)

Therefore,

\(= \cfrac{b^2}{ac}\)

Answer 8

Thanks!

Answer 9

You're welcome :)

Answer 10

I didn't get the second step