Question

oblicz postać iloczynowa wielomianu p(x)=(1+x)(2x-5)-(5-2x)(x-2)

Answer 1

p(x) = (1 +x)(2x -5) - (5 -2x)(x - 2) =

= 2x -5 +2x^2 - 5x - [5x - 10 -2x^2 + 4x] =

= 2x^2 -3x - 5 - 9x +10 + 2 x^2 =

= 4 x^2 - 12 x + 5

delta = (-12)^2 - 4*4*5 = 144 - 80 = 64

p64 = 8

x1 = [12 - 8]/8 = 4/8 = 0,5

x2 = [12 +8]/8 = 20/8 = 2,5

zatem

p(x) = 4*(x - 0,5)*9x - 2,5)

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korzystamy z wzoru :

ax^2 + bx + c = a*( x -x1)*(x - x2)