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The ratio of roots of $x^2+bx+c=0$ is same as the ratio of the roots of $x^2+qx+r=0$. Then which of the following is true?

$\begin{array}{1 1}(A) \;br^2=qc^2 \\(B)\;cr^2=qb^2\\(C)\;rc^2=bq^2\\(D)\;rb^2=cq^2 \end{array}$

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  • $(a-b)^2=(a+b)^2-4ab$
Let the roots of $x^2+bx+c=0$ be $\alpha_1\:and\:\beta_1$
and the roots of $x^2+qx+r=0$ be $\alpha_2\:and\:\beta_2$
$\Rightarrow\:\alpha_1+\beta_1=-b$, $ \alpha_1\beta_1=c$ and
Given: The ratio of the roots of
$x^2+bx+c=0\:\:and\:\:x^2+qx+r=0$ are same
using componendo and dividendo
Squaring both the sides,
answered Jul 26, 2013 by rvidyagovindarajan_1

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