Question

Find a quadratic polynomial whose zeroes are reciprocals of the zeroes of the polynomial f(x) = ax² + bx + c, a ≠ 0, c ≠ 0.

Answer 1

Let α and β be zero of the given polynomial ax² + bx + c

∴ `α + β = - b/a` and `αβ = c/a`

`s = 1/α + 1/β`

= `(β + α)/(αβ)`

= `(- b/a)/(c/a)`

= `(-b)/c`

`p = 1/α * 1/β`

= `1/(αβ)`

= `a/c`

The required polynomial, x² – sx + p or cx² + bx + a.