SCI 113
Demo Equation Solving

<<Graphics`ImplicitPlot`

Polynomial Equations

Solve[a x+b==0,x]

Solve[a (x^2)+b x+c==0,x]

Solve[a (x^3)+b (x^2)+c x+d==0,x]

Solve[a (x^4)+b (x^3)+c (x^2)+d x+e==0,x]

Solve[a (x^5)+b (x^4)+c (x^3)+d (x^2)+e x+f==0,x]

Solve[(x^5)-3 (x^2)-5 x+2==0,x]

Plot[(x^5)-3 (x^2)-5 x+2,{x,-2,2}]

Newton-Raphson procedure

f[x_]:=(x^2)-10

r[x_]=x-((f[x])/(f'[x]))

N[NestList[r,1,10],40]//TableForm

Equations in several variables

ImplicitPlot[{y+2 x==3,-y+x==1},{x,-1,2}]

Solve[{y+2 x==3,-y+x==1},{x,y}]

ImplicitPlot[{(x^2)+(y^2)==2,(((x-1))^2)+(((y-1))^2)==2},{x,-2,3}]

Solve[{(x^2)+(y^2)==2,(((x-1))^2)+(((y-1))^2)==2},{x,y}]

ImplicitPlot[{y ((x^2)+1)==x,(((x-1))^2)+(y^2)==1},{x,-1,3}]

NSolve[{y ((x^2)+1)==x,(((x-1))^2)+(y^2)==1},{x,y}]