Question

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then \(\frac{1}{\alpha}\)+ \(\frac{1}{\beta}\)+\(\frac{1}{\gamma}\) =

A. - \(\frac{b}{d}\)

B. \(\frac{c}{d}\)

C. -\(\frac{c}{d}\)

D. -\(\frac{c}{a}\)

Answer 1

Given,

f(x) = ax³ + bx² + cx + d,

As we know,

α + β + y = b/a

αβ + βy + yα = – c/a …………….(i)

αβy = d/a ……………….. (ii)

Now, Divide (i) by (ii)

We get

  \(\frac{1}{\alpha}\)+ \(\frac{1}{\beta}\)+\(\frac{1}{\gamma}\)= – c/d