Complex Numbers And Quadratic Equations question 576
Question: If $ a{{(p+q)}^{2}}+2bpq+c=0 $ and $ a{{(p+r)}^{2}}+2bpr+c=0 $ , then $ qr $ =
Options:
A) $ p^{2}+\frac{c}{a} $
B) $ p^{2}+\frac{a}{c} $
C) $ p^{2}+\frac{a}{b} $
D) $ p^{2}+\frac{b}{a} $
Show Answer
Answer:
Correct Answer: A
Solution:
From the given equations, we find that q and r are roots of the equation $ a{{(p+x)}^{2}}+2bpx+c=0 $ or $ ax^{2}+2x(a+b)p+ap^{2}+c=0 $ . Now product of the roots is $ qr=\frac{ap^{2}+c}{a}=p^{2}+\frac{c}{a} $ .
BETA
