Complex Numbers And Quadratic Equations question 567
Question: If the ratio of the roots of $ ax^{2}+2bx+c=0 $ is same as the ratio of the roots of $ px^{2}+2qx+r=0 $ , then [Pb. CET 1991]
Options:
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
Show Answer
Answer:
Correct Answer: B
Solution:
If the roots of equation $ ax^{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 $ px^{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} $ .
BETA
