If α ,   β ,   γ are the roots of x 3 - 2 x 2 + 3 x - 4 = 0 , then find ∑ α β ( α + β )

Step-by-step solution

x 3 - 2 x 2 + 3 x - 4 = 0   α β γ α + β + γ = 2 α β γ = 4 , ∑ α β = 3 α β ( α + β ) + β γ ( β + γ ) + γ α ( γ + α ) α β ( 2 - γ ) + β γ ( 2 - α ) + γ α ( 2 - β ) = 2 ∑ α β - 3 α β γ = 2 ( 3 ) - 3 × 4 = - 6