#f(x)=x^4+3x^2-4x#
#color(white)(f(x))=x(x^3+3x-4)#
#"the coefficients of "x^3+3x-4#
#1+3-4=0rArrx=1" is a root and "(x-1)" is a factor"#
#color(red)(x^2)(x-1)color(magenta)(+x^2)+3x-4#
#=color(red)(x^2)(x-1)color(red)(+x)(x-1)color(magenta)(+x)+3x-4#
#=color(red)(x^2)(x-1)color(red)(+x)(x-1)color(red)(+4)(x-1)cancel(color(magenta)(+4))cancel(-4)#
#=color(red)(x^2)(x-1)color(red)(+x)(x-1)color(red)(+4)(x-1)+0#
#rArrx(x-1)(x^2+x+4)=0#
#rArrx=0,x=1to("with multiplicity of 1")#
#"check the "color(blue)"discriminant "" of "x^2+x+4#
#"with "a=1,b=1,c=4#
#Delta=b^2-4ac=1-16=-15#
#"indicating there are 2 complex roots"#
#"using the "color(blue)"quadratic formula"#
#x=(-1+-sqrt(-15))/2#
#rArrx=-1/2+-sqrt15/2i#
#"there are 2 real zeros and 2 complex zeros"#
