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Question Number 121918 by greg_ed last updated on 12/Nov/20

a, b a n d c a r e s o l u t i o n s o f x^{3} - 4 x^{2} - 5 x + 8 = 0 .

W i t h o u t d e t e r m i n a t i n g a, b a n d c;

c a l c u l a t e a + b + c .

Commented by mr W last updated on 12/Nov/20

a + b + c = 4

a b + b c + c a = - 5

a b c = - 8

Commented by greg_ed last updated on 12/Nov/20

please, mr W : {it}^{'} s not very very clear for

me!

Commented by physicstutes last updated on 12/Nov/20

Generally if α, β and γ are roots of the equation,

{a x}^{3} + {b x}^{2} + c x + d = 0

then α + β + γ = - \frac{b}{a}

α β γ = - \frac{d}{a}

Commented by greg_ed last updated on 12/Nov/20

thanks, physicstutes!

Commented by MJS_new last updated on 12/Nov/20

(x - a) (x - b) (x - c) = 0

x^{3} - (a + b + c) x^{2} + (a b + a c + b c) x - a b c = 0

x^{3} - 4 x^{2} + (- 5) x - (- 8) = 0

Commented by greg_ed last updated on 12/Nov/20

ok, MJS_new! {it}^{'} s cool!

Answered by Dwaipayan Shikari last updated on 12/Nov/20

f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + \dots + a_{n} = 0

I n t h i s p o l y n o m i a l s u m o f t h e r o o t s i s (- \frac{a_{1}}{a_{0}})

h e r e p o l y n o m i a l i s x^{3} - 4 x^{2} - 5 x + 8 = 0

s u m o f t h e r o o t s = - (- \frac{4}{1}) = 4

Commented by greg_ed last updated on 12/Nov/20

thanks, Dwaipayan Shikari!

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