Rozkład wielomianów na czynniki: w(x)= -6x³-12x² -6x = -6x(x² + 2x + 1) -6x(x² + 2x + 1) -6x = 0/: (-6) x = 0 x² + 2x + 1= 0 a= 1 b= 2 c = 1 Δ = b² -4ac = 2² - 4*1*1 = 4 - 4 = 0 Jesli Δ = 0 , to x1 = x2 = -b/ 2a x1 = -b/2a x1 = -2 / 2*1 = -2 : 2 = -1 x2 = -1 odp. x1= -1, x2 = -1, x3 = 0 /////////////////////////////////////// w(x)= 20x⁵+14x⁴+2x³ = 2x³(10x² + 7x + 1) 2x³ = 0 x1 = 0 10x² + 7x + 1 = 0 a = 10 b = 7 c =1 Δ = b² - 4ac = 7² - 4* 10 * 1 = 49 - 40 = 9 √Δ = √9 Δ = 3 x2 = (-b - √Δ ) : 2a x2 = (-7 - 3 ) : 2 *10 x2 = -10 : 20 = -1/2 x3 = (-b+ √Δ ) : 2a x3 = (-7 + 3 ) : 2 *10 x3 = -4 : 20 = -1/5 Odp. x1 =0, x2 = -1/2, x3 = -1/5 ///////////////////////////////////////// Rozwiąż równanie wielomianowe x³-4x² -9x+36=0 (x³-4x²) + ( -9x+36) = 0 x²(x - 4) - 9(x - 4) = 0 (x² - 9)² (x-4)² = 0 Przydatna strona : http://matematyka.pisz.pl/strona/118.html
