403 MrG Complex Roots

2468 days ago by MATH4R2013

#1) Find a polynomial equation of Degree 5 with roots {1,5i,1+i,?,?} #1) ANS: roots are {1,5i,1+i,-5i,1-i} #1) ANS: factors are (x-1),(x-5i),(x-(1+i)),(x+5i)(x-(1-i)) #1) ANS: x^5-3*x^4+29*x^3-77*x^2+100*x-50==0 show(expand((x-5*i)*(x+5*i))) show(expand(x-(1+i))*(x-(1-i)).simplify_radical()) show(expand((x+i-1)*(x-i-1))) 
       


show(expand((x-1)*(x^2+25))) show(expand((x^3-x^2+25*x-25)*(x^2-2*x+2))) 
       

factor(x^5-3*x^4+29*x^3-77*x^2+100*x-50) 
       
solve(x^5-3*x^4+29*x^3-77*x^2+100*x-50==0,x) 
       
plot(x^5-3*x^4+29*x^3-77*x^2+100*x-50,-2,2)