Answer:
2/3.
Explanation:
α + β + γ = -b/a
αβ + βγ + γ α = c/a
αβγ = -d/a
These are the relation between the roots α, β and γ and the coefficients of the cubic equation:
P(x) = ax^3 + bx^2 + cx + d
Our equation is:
P(x) = 4x³ – x² − 6x + 9
So, for the above equation:
a + b + c = -(-1)/4 = 1/4
ab + ac + bc = -6/4 = -3/2
abc = -9/4.
1/a + 1/b + 1/c
= (bc + ac + ab) / abc
So, plugging in the above values:
this = (-3/2) / (-9/4)
= 3/2 * 4/9
= 12/18
= 2/3.