If α, β and γ are the roots of the equation

Question

x^3-2x^2+3x-4=0 then 1/α+1/β+1/γ=?  

 

 

Answer 1

Sum of product rule :

If α, β, and γ are the roots of the polynomial ax³ + bx² + cx + d = 0, then,

Product of roots : αβγ = - constant term / coefficient of x³  = - d/a, and

Sum of products : αβ + βγ + αγ = coefficient of x / coefficient of x³ = c/a .

The equation is x³ - 2x² + 3x - 4 = 0.

αβγ = - constant term / coefficient of x³ = - (- 4)/1 =  4, and

αβ + βγ + αγ = coefficient of x / coefficient of x³ = 3/1 = 3.

⇒1/α + 1/β + 1/γ = (αβ + βγ + αγ)/αβγ

= 3/4.

Therefore, 1/α + 1/β + 1/γ = 3/4.