question_answer

A quadratic polynomial\[f(x)={{x}^{2}}-(m+n)x+mn\] has two zeros. Find the value of\[{{\alpha }^{2}}{{\beta }^{2}}\].

A)  \[\frac{1}{4}\left( {{m}^{2}}+{{n}^{2}} \right)\]                   

B)  \[\frac{1}{6}\left( {{m}^{2}}+4{{n}^{3}} \right)\]

C)  \[{{m}^{2}}+{{n}^{2}}\]

D)  \[\frac{1}{8}\left( {{m}^{2}}+4{{n}^{2}} \right)\]