Question

If α, β are the zeros of the polynomial ax² + bx + c, then (α² + β²) = ?

(a) $\frac{a^2-2bc}{b^2}$
(b) $\frac{b^2-2ac}{a^2}$
(c) $\frac{a^2+2bc}{b^2}$
(d) $\frac{b^2+2ac}{a^2}$

Answer 1

$$\begin{gathered} \left(b\right)\frac{b^2-2ac}{a^2} \\ \text{Here,}\mathrm{\alpha }\text{+}\mathrm{\beta }\text{=}\frac{-b}{a}\text{and}\mathrm{\alpha \beta }\text{=}\frac{c}{a} \\ \therefore ({\mathrm{\alpha }}^2+{\mathrm{\beta }}^2)={(\mathrm{\alpha }+\mathrm{\beta })}^2-2\mathrm{\alpha \beta } \\ =\frac{b^2}{a^2}-\frac{2c}{a}=\frac{b^2-2ac}{a^2} \end{gathered}$$