zad1 a) x3+7x2=0 x2(x+7)=0 x2=0 v x+7=0 x=0 v x=-7 b)2x4-3x3=0 x3(2x-3)=0 x3=0 v 2x-3=0 x=0 v 2x=3/2 x =3/2=1,5 c)12x2=24x3 12x2-24x3=0 12x2(1-12x)=0 12x2=0/12 v 1-12x=0 x2=0 v -12x=-1/-12 x=0 v x=1/12 d) x5=121x3 X5-121X3=0 x3(x2-121)=0 x3=0 v (x-11)=0 v (x+11)=0 x=11 v x =-11 e)x3+5x=0 x(x2+5)=0 x=0 v( x+pierwoastek 5)=0 v (x -pierwiastek 5) x=pierwiastek5 v x=- pierwiastek5 f)x4-8x2=0 x2(x2-8)=0 x2=0 v (x-pierwiastek 8) v (x+pierwiastek 8) x=0 v x =pierwiastek 8 v x=- pierwiastek 8 ZAD2 a)x3+x2-12x=0 x(x2+x-12)=0 x=0 v x2+x-12=0 v delta = 1 +48 delta=49 pierwiastek z delty = 7 x1= -4 v x2=3 b)x4+6x3+5x2=0 x2(x2+6x+5)=0 x2=0 v x2+6x+5 =0 x=0 v pierwiastek z delty =16 x1=-11 v x2 =5 c)2x3+5x2+2x=0 x(2x2+5x+2)=0 x=0 v pierwiastek delty =3 x1=-2 v x2=-1/2 d)7x3+2x=x2 7x3+2x-x2=0 x(7x2+2-1)=0 x=0 v 7x2-1=0 x=0 v 7x2=1/7 v x2=1/7 x = pierwiastek 1/7 e)3x4+1/4x3=x4 3x4+1/4x3-x4=0 x3(3x+1/4-x)=0 x3=0 v 2x+1/4=0 x=0 v 2x=-1/4 /;2 x=-1/4* 1/2 g)x3-pierwiastek z 2x2-7x=0 x3-pierwastek z 2x3-7x=0 x(x2-pierwiateks 2 x2-7)=0 x=0 v -pierwiastek 2 x2 - 7 =0 pierwiastek 2 x2 = 7 / pierwiatesk 2 x2=7pierwiastkow 2 h)x5+x4+2x3=0 x3(x2+x+2)=0 x3+0 v x2+x+2=0 delta =b2-4*ac delta= 1 - 4*1*2 delta 1 -8 delta -7 brak pierwiastkow
