A) \[{{c}^{2}}\left( \frac{c+25}{{{a}^{3}}} \right)\]
B) \[{{c}^{3}}{{\left( \frac{c-25}{{{a}^{2}}} \right)}^{2}}\]
C) \[\frac{b{{c}^{3}}}{{{a}^{3}}}\]
D) \[\frac{b{{c}^{2}}}{a}\]
E) \[{{c}^{2}}\left( \frac{c-25}{{{a}^{3}}} \right)\]
Correct Answer: A
Solution :
Since,\[p,q\]are the roots of the equation \[a{{x}^{2}}-25x+c=0\] \[\therefore \] \[p+q=\frac{20}{a},pq=\frac{c}{a}\] \[{{p}^{3}}{{q}^{3}}+{{p}^{2}}{{q}^{3}}+{{p}^{3}}{{q}^{2}}\] \[\Rightarrow \] \[{{p}^{2}}{{q}^{2}}(pq+p+q)\] \[\Rightarrow \] \[{{p}^{2}}{{q}^{2}}(pq+p+q)\] \[\Rightarrow \] \[\frac{{{c}^{2}}}{{{a}^{2}}}\left( \frac{c}{a}+\frac{25}{a} \right)=\frac{{{c}^{2}}(c+25)}{{{a}^{3}}}\]
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