MATLAB: Numerically solve for x in a polynomial equation

polynomial

If I have a 3rd order polynomial (y = ax^3 + bx^2 + cx + d) with all the coefficients known, how do I plug in a y number and get out the x number?

Write the polynomial as

a*x^3+b*x^2+c*x+d-y

Then you can use fzero to solve x.

doc fzero

x''''=A*x+B*y+C*(D*y+E*x+F*x'''') -> x''''=((A+C*E)*x+(B+C*D)*y)/(1-C*F)
y''''=D*y+E*x+F*(A*x+B*y+C*y'''') -> y''''=((E+A*F)*x+(D+B*F)*y)/(1-C*F)

Best wishes

Torsten.

If the last term is Z * x^(-P), then multiply the equation by x^P, transforming it into

a*x^(P-1) + b*x^(P-2) + c*x^(P-3) + .... Z = 0

then you can use roots()

If you think about this for a second, you can see that you can skip the roots() step if your coefficients are arranged in the right order.