Complex Numbers And Quadratic Equations question 460
Question: If $ a{{(p+q)}^{2}}+2bpq+c=0anda{{(p+r)}^{2}}+2bpr+c=0(a\ne 0), $ then
Options:
A) $ qr=p^{2} $
B) $ qr=p^{2}+\frac{c}{a} $
C) $ qr=-p^{2} $
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Given, $ a{{(p+q)}^{2}}+2bpq+c=0 $ and $ a{{(p+r)}^{2}}+2bpr+c=0 $
$ \Rightarrow q $ and r satisfy the equation $ a{{(p+x)}^{2}}+2bpx+c=0 $
$ \Rightarrow q $ and r are the roots of $ ax^{2}+2(ap+bp)x+c+ap^{2}=0 $
$ \Rightarrow qr= $ product of roots $ =\frac{c+ap^{2}}{a}=p^{2}+\frac{c}{a} $
BETA
