Question

If α, β are the zeros of the polynomial f(x) = ax² + bx + c, then \(\frac{1}{\alpha^2}\) + \(\frac{1}{\beta^2}\) =

A. \(\frac{b^2-2ac}{a^2}\)

B. \(\frac{b^2-2ac}{c^2}\)

C. \(\frac{b^2+2ac}{a^2}\)

D. \(\frac{b^2+2ac}{c^2}\)

Answer 1

Given

f(x) = ax² + bx + c

α, β are the Zeros

α + β = – b/a

αβ = c/a

1/ α + 1/β = \(\cfrac{\frac{b}{a}}{\frac{c}{a}}\)

1/α² + 1/β²

= (1/α + 1/β)² – 2/αβ

= ( – b/c)² – 2a/c

= \(\frac{b^2-2ac}{c^2}\)