Complex Numbers And Quadratic Equations question 529
Question: If the ratio of the roots of the equation $ ax^{2}+bx+c=0 $ be $ p:q $ , then [Pb. CET 1994]
Options:
A) $ pqb^{2}+{{(p+q)}^{2}}ac=0 $
B) $ pqb^{2}-{{(p+q)}^{2}}ac=0 $
C) $ pqa^{2}-{{(p+q)}^{2}}bc=0 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ p\alpha ,q\alpha $ be the roots of the given equation $ ax^{2}+bx+c=0 $ . Then $ p\alpha +q\alpha =-\frac{b}{a} $ and $ p\alpha .q\alpha =\frac{c}{a} $ From first relation, $ \alpha =-\frac{b}{a(p+q)} $ Substituting this value of $ \alpha $ in second relation, we get $ \frac{b^{2}}{a^{2}{{(p+q)}^{2}}}\times pq=\frac{c}{a} $ Þ $ b^{2}pq-ac{{(p+q)}^{2}}=0 $ Note: Students should remember this question as a fact.
BETA
