Question

rozwiąż rówania wielomianoe:

2x²+8x²+3x+12=0

x³-2x²-4x+8=0

x³+3x²-x-3=0

-x³+5x²-x+5=0

Answer 1

2x³+8x²+3x+12 = 0

2x²(x+4)+3(x+4) = 0

(2x²+3)(x+4) = 0

2x²+3 > 0

x+4 = 0

x = -4

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x³-2x²-4x+8 = 0

x²(x-2)-4(x-2) = 0

(x²-4)(x-2) = 0

(x+2)(x-2)(x-2) = 0

x+2 = 0  => x = -2

lub

x-2 = 0   => x = 2

Odp. x = -2   v   x = 2

 

x³+3x²-x-3 = 0

x²(x+3)-(x+3) = 0

(x+3)(x²-1) = 0

(x+3)(x+1)(x-1) = 0

x+3 = 0   => x = -3

lub

x+1 = 0   => x = -1

lub

x-1 = 0   = x = 1

Odp. x = -3   v   x = -1   v   x = 1 

 

-x³+5x²-x+5 = 0

x²(-x+5)+(-x+5) = 0

(x²+1)(-x+5) = 0

x²+1 > 0

-x+5 = 0   

-x = -5

x = 5

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