Question

If alfa ,beta,gama are the zeroes of the polynomial 6x cube +3x square - 5x +1, than find the value of alfa _1 + beta_1+ gama-1

Answer 1

$6 x^{3}+3 x^{2} -5x+1$ 
a=6 , b=3 , c=-5 , d=1
Roots are α , β and γ.
α+β+γ= $- \frac{b}{a}$=-3/6=-1/2
αβ+βγ+γα= $\frac{c}{a}$=-5/6
αβγ=$- \frac{d}{a}$=-1/6

$\alpha ^{-1}+ \beta ^{-1}+\gamma^{-1}$ = αβ+βγ+γα / αβγ
= $\frac{ \frac{-5}{6}}{\frac{-1}{6}}$
=5