A) \[\frac{b}{ac}=\frac{q}{pr}\]
B) \[\frac{{{b}^{2}}}{ac}=\frac{{{q}^{2}}}{pr}\]
C) \[\frac{2b}{ac}=\frac{{{q}^{2}}}{pr}\]
D) None of these
Correct Answer: B
Solution :
If the roots of equation \[a{{x}^{2}}+2bx+c=0\]are in the ratio m : n, Then we have \[mn{{(2b)}^{2}}={{(m+n)}^{2}}ac\] .....(i) Also if the roots of the equation \[p{{x}^{2}}+2qx+r=0\]are also in the same ratio \[m:n\], then \[mn{{(2q)}^{2}}={{(m+n)}^{2}}pr\] .....(ii) Dividing (i) and (ii), we get \[\frac{{{b}^{2}}}{{{q}^{2}}}=\frac{(ac)}{(pr)}\]or \[\frac{{{b}^{2}}}{ac}=\frac{{{q}^{2}}}{pr}\].
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