A) \[{{a}^{2}}{{x}^{2}}-\left( {{b}^{2}}-2ac \right)x+{{c}^{2}}=0\]
B) \[\left( {{a}^{2}}-r \right){{x}^{2}}+\left( {{b}^{2}}-r \right)x+{{c}^{2}}r=0\]
C) \[\left( {{a}^{2}}-ac \right){{x}^{2}}+\left( {{b}^{2}}+2ac \right)x+{{c}^{2}}=0\]
D) \[2{{a}^{2}}{{x}^{2}}-\left( {{b}^{2}}+2ac \right)x+2{{c}^{2}}=0\]
Correct Answer: A
Solution :
(a): \[E{{q}^{n}}\] with roots \[{{\alpha }^{2}},{{\beta }^{2}}\] is: \[{{x}^{2}}\left( {{\alpha }^{2}}+{{\beta }^{2}} \right)x+{{\alpha }^{2}}{{\beta }^{2}}=0\] \[\Rightarrow {{x}^{2}}-\left\{ {{(\alpha +\beta )}^{2}}-2\alpha \beta \right\}x+{{\alpha }^{2}}{{\beta }^{2}}=0\] \[\Rightarrow {{x}^{2}}-\left\{ \frac{{{b}^{2}}}{{{a}^{2}}}-\frac{2c}{a} \right\}x+\frac{{{c}^{2}}}{{{a}^{2}}}=0\]
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