Question

If α, β, γ are the zeros of the polynomial f(x) = ax³ + bx² + cx + d, then α² + β² + γ² =

A. \(\frac{b^2-ac}{a^2}\)

B. \(\frac{b^2-2ac}{a}\)

C. \(\frac{b^2+2ac}{b^2}\)

D. \(\frac{b^2+2ac}{a^2}\)

Answer 1

f(x) = ax³ + bx² + cx + d,

Then the roots are :

α , β and γ

Now, sum of roots:

α + β + γ = - b/a ….(i)

The product of zeroes,

α × β × γ = - d/a….(ii)

And,

αβ + βγ + γα = c/a…(iii)

Now,

(α + β + γ)² = α² + β² + γ² + 2αβ + 2βγ + 2γα