Question

If α and β are the zeroes of the polynomial f(x)=ax^2 + bx + c, then find 1/α^2 + 1/β^2​

Answer 1

f(x) = ax² + bx + c

α, β are the Zeros

α + β = – b/a

αβ = c/a

1/ α + 1/β = $\huge \sf \frac{ \frac{b}{a} }{ \frac{c}{a} }$

$\:$

1/α² + 1/β²

= (1/α + 1/β)² – 2/αβ

= ( – b/c)² – 2a/c

$\implies\large\sf\frac{ {b}^{2} - 2ac }{ {c}^{2} }$

Answer 2

Step-by-step explanation:

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