A) \[qr={{p}^{2}}\]
B) \[qr={{p}^{2}}+\frac{c}{a}\]
C) \[qr=-{{p}^{2}}\]
D) none of these
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 \[a{{x}^{2}}+2(ap+bp)x+c+a{{p}^{2}}=0\] |
\[\Rightarrow qr=\]product of roots \[=\frac{c+a{{p}^{2}}}{a}={{p}^{2}}+\frac{c}{a}\] |
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