If `alpha,beta` are the zeros of the polynomial `f(x)=a x^2+b x+c ,` then `1/(alpha^2)+1/(beta^2)=` (a) `(b^2-2a c)/(a^2)` (b) `(b^2-2a c)/(c^2)` (c) `(b^2+2a c)/(a^2)` (d) `(b^2+2a c)/(c^2)`

Explanation

Given that `alpha and beta` are the zeroes of polynomial `f(x) = ax^2 + bx + c`.

Sum of roots = `alpha + beta = -b/a`

Product of roots = `alpha beta = c/a`

`therefore alpha^2 + beta^2 = (alpha + beta)^2 – 2 alpha beta = (-b/a)^2 – 2 * c/a= (b^2 – 2ac)/a^2`

`implies 1/alpha^2 + 1/beta^2 = (alpha^2 + beta^2)/(alpha^2 beta^2) = (b^2 – 2ac)/a^2 * a^2/c^2 = (b^2 – 2ac)/c^2`

Hence, the correct answer is option B.