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If the ratio of the roots of x^2 + bx + ...

If the ratio of the roots of `x^2 + bx + c =0` and ` x^2 + qx + r = 0` is same then

Text Solution

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Let `alpha,beta` are the roots of `x^2+bx+c = 0`
Then, `alpha+beta =-b` and `alphabeta = c`
Let `A,B` are the roots of `x^2+qx+r = 0`
Then, `A+B =-q` and `AB = r`
We are given,
`alpha/beta = A/B->(1)`
`=>beta/alpha = B/A->(2)`
Adding (1) and (2),
...
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