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(D) Given that $\alpha$ and $\beta$ are the roots of the quadratic equation $a x^{2}+b x+c=0$.According to the relationship between roots and coeffici

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$\frac{b^{2}-2 a c}{a^{2}}$

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(D) Given that $\alpha$ and $\beta$ are the roots of the quadratic equation $a x^{2}+b x+c=0$.According to the relationship between roots and coefficients:Sum of roots: $\alpha+\beta = -\frac{b}{a}$Product of roots: $\alpha \beta = \frac{c}{a}$We know the algebraic identity: $\alpha^{2}+\beta^{2} = (\alpha+\beta)^{2} - 2 \alpha \beta$Substituting the values:$\alpha^{2}+\beta^{2} = \left(-\frac{b}{a}\right)^{2} - 2\left(\frac{c}{a}\right)$$= \frac{b^{2}}{a^{2}} - \frac{2c}{a}$$= \frac{b^{2} - 2ac}{a^{2}}$

If $\alpha$ and $\beta$ are the roots of the equation $a x^{2}+b x+c=0$,find the value of $\alpha^{2}+\beta^{2}$.

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