Question 1132136


{{{3x^3+2x^2+75x-50=0  }}}


use Newton-Raphson

{{{x[n+1]=x[n]-f(x)/f’(x)}}}

{{{f}}}’{{{(x)=9x^2+4x+75}}}


Let {{{x[1] =1}}}

than {{{x[2] =1-(3*1^3+2*1^2+75*1-50)/(9*1^2+4*1+75)}}}

 {{{x[2] =1-(3+2+75-50)/(9+4+75)}}}

 {{{x[2] =1-30/88}}}

{{{ x[2] =88/88-30/88}}}

{{{ x[2] =58/88}}}

{{{x[2] =0.659091}}}


{{{x[3]=0.659091-(3*0.659091^3+2*0.659091^2+75*0.659091-50)/(9*0.659091^2+4*0.659091+75)}}}

{{{x[3]=0.659091-(1.159556154817871713)/(81.545972516529)}}}

{{{x[3]=0.659091-0.01422}}}

{{{x[3]}}} ≈ {{{0.644871}}}=> one real solution


you also have complex roots:

{{{x}}}≈{{{-0.6558 - 5.0414* i}}}

{{{x}}}≈{{{-0.6558 +5.0414 *i}}}