question_answer

If\[\alpha \]and\[\beta \]are the roots of the polynomial\[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{bx}+\mathbf{c}\], then find the value of\[{{\alpha }^{\mathbf{2}}}+{{\beta }^{\mathbf{2}}}\]

A) \[\frac{{{b}^{2}}-2ac}{{{a}^{2}}}\] 

B) \[\frac{b+2ac}{a}\]

C) \[\frac{b-2ac}{a}\]        

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

E) None of these