z.1 W(x) - P(x)*Q(x) = [3x^3 + x^2 +1] -[(x+3)(x^2 - 3)] = = [3x^3 + x^2 +1]- [ x^3 +3x^2 - 3x - 9] = 2x^3 -2x^2 +3x + 10 ------------------------------------------------------------------------ z.2 a) x^3 - 7 x^2 - 4x + 28 = 0 x^2*( x - 7) - 4*(x - 7) = 0 (x^2 - 4)*(x -7) = 0 (x -2)*(x +2) *(x - 7) = 0 x1 = -2, x2 = 2, x3 = 7 ------------------------------------ b) (x^2 - 3x)*(x^2 -4)*(x^2 + 4x + 4) = 0 x*( x -3)*(x-2)*(x +2)*(x+2)^2 = 0 x1 = -2 - potrójny x2 = 0 x3 = 2 x4 = 3 ---------------------------------------------- c) x^3 - 3 x^2 - 4x + 12 = 0 x^2*(x - 3) - 4*(x - 3) = 0 (x^2 - 4)*(x -3) = 0 (x -2)*(x +2)*(x -3) = 0 x1 = -2 x2 = 2 x3 = 3 ---------------------------------------------------- d) -2x*(x - 1)*(x +3) = 0 x1 = -3 x2 = 0 x3 = 1 ==========================================
Zad. 1) Dane: W(x) = 3x³ + x² + 1 P(x) = x + 3 Q(x) = x² - 3 W(x) - P(x)*Q(x) = ? W(x) - P(x)*Q(x) = 3x³ + x² + 1 - (x + 3)(x² - 3) = = 3x³ + x² + 1 - (x³ - 3x + 3x² - 9) = = 3x³ + x² + 1 - x³ + 3x - 3x² + 9 = = 2x³ - 2x² + 3x + 10 Zad. 2) a) x³ - 7x² - 4x + 28 = 0 x²(x - 7) - 4(x - 7) = 0 (x² - 4)(x - 7) =0 (x + 4)(x - 4)(x - 7) = 0 x + 4 = 0 ∨ x - 4 = 0 ∨ x - 7 = 0 x = - 4 ∨ x = 4 ∨ x = 7 b) (x² + 3x)(x² - 4)(x² + 4x + 4) = 0 x(x + 3)(x + 2)(x - 2)(x + 2)² = 0 x = 0 ∨ x + 3 = 0 ∨ x + 2 = 0 ∨ x - 2 = 0 x = 0 ∨ x = - 3 ∨ x = - 2 ∨ x = 2 c) x² - 3x² - 4x + 12 = 0 - 2x² - 4x + 12 = 0 / :( - 2) x² + 2x - 6 = 0 (x² + 2x + 1) - 1 - 6 = 0 (x + 1)² - 7 = 0 (x + 1 - √7)(x + 1 + √7) = 0 x + 1 - √7 = 0 ∨ x + 1 + √7 = 0 x = √7 - 1 ∨ x = - √7 - 1 d) - 2x(x - 1)(x + 3) = 0 - 2x = 0 ∨ x - 1 = 0 ∨ x + 3 = 0 x = 0 ∨ x = - 3 ∨ x = 1
zad 1 3x³ + x² + 1 - (x + 3)(x² - 3) = = 3x³ + x² + 1 - x³ + 3x - 3x² + 9 = = 2x³ - 2x² + 3x + 10 zad 2 a)x³ - 7 x² - 4x + 28 = 0 x²( x - 7) - 4(x - 7) = 0 (x² - 4)(x -7) = 0 (x -2)(x +2) (x - 7) = 0 x-2=0 x=2 x+2=0 x=-2 x-7=0 x=-7 b)(x² + 3x)(x² - 4)(x² + 4x + 4) = 0 x(x + 3)(x + 2)(x - 2)(x + 2)² = 0 x = 0 x+3=0 x=-3 x+2=0 x=-2 x-2=0 x=2 x+2=0 x=-2 k=2 c)x³ - 3 x² - 4x + 12 = 0 x² (x - 3) - 4(x - 3) = 0 (x² - 4)(x -3) = 0 x²-4=0 x²=4 x=2 lub x=-2 x-3=0 x=3 d)-2x(x-1)(x+3)=0 -2x=0 x=0 x-1=0 x=1 x+3=0 x=-3
