question_answer

If \[\alpha \]and \[\beta \] are the zeroes of the quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c,\] then the value of \[{{\alpha }^{4}}+{{\beta }^{4}}\] is:

A) \[\frac{{{({{b}^{2}}-2ac)}^{2}}+{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\]

B) \[\frac{{{({{b}^{2}}+2ac)}^{2}}-{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\]

C) \[\frac{{{({{b}^{2}}-2ac)}^{2}}-2{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\]

D) \[\frac{{{({{b}^{2}}+2ac)}^{2}}+2{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\]