Question

2x3 + 7x2 + 7x +2 = 0 rozwiąż równanie

Answer 1

2x3 + 7x2 + 7x +2 = 0

2x^3 + 2 + 7x^2 + 7x = 0

2(x^3 + 1) + 7x(x + 1) = 0

2(x + 1)(x^2 - x + 1) + 7x(x  +1) = 0

(x + 1) (2x^2 - 2x + 2 + 7x) = 0

x + 1 = 0    lub   2x^2 + 5x + 2 = 0

 x = -1                   Δ = 25 - 16 = 9

                             √Δ = 3

                             x1 = (-5 - 3)/4 = - 8/4 = -2

                             x2 = (-5 + 3) /4 = - 2/4 = -1/2

 

odp. x = -1   lub   x =  -2   lub   x = -1/2

Answer 2

szukamy pierwiastków wsród dzielników 2

D(2)=-1,1,-2,2

W(-1)=2×(-1)³+7×(-1)²+7×(-1)+2=0

 

 

(2x³+7x²+7x+2):(x+1)= 2x²+5x+2

-2x³-2x²

...............

=== 5x²+7x+2

      -5x²-5x

......................

      ==  2x+2

           -2x-2

.......................

==============

Δ=25-16=9

x₁=[-5-3]/4=-2

x₂=[-5+3]/4=-½

 

2x³+7x²+7x+2=(x+1)(2x²+5x+2)    =2(x+½)(x+2)(x+1)

   

odp.:

x=-1  lub x=-½   lub x=-2