SOLUTION: The equation of y=x³+4x²+x-6 has roots α, β and γ. Find the value of
(i) α²+β²+γ²
(ii) α²β²γ²
(iii) (α+β)(β+γ)
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Question 1132057: The equation of y=x³+4x²+x-6 has roots α, β and γ. Find the value of
(i) α²+β²+γ²
(ii) α²β²γ²
(iii) (α+β)(β+γ)(γ+α)
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
x^3+4x^2+x-6=0
with synthetic division, using -3
1-----4----1---- -6
1-----1--- -2-----0
(x+3)(x^2+x-2)=0, so -3 is a root
(x+3)(x+2)(x-1)=0
roots are -3, -2, and +1
(i) is 14
(ii) is 36
(iii) is (-5)(-1)(-2)=-10
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
The equation of has roots , and }.
Find the value of
(i)
(ii)
(iii)
.......factor completely
solutions:
=> let's , and }
then,
(i)
(ii)
(iii)
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