1.

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»

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} }


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