Question

Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) = x4 + 3x3 - 5x2 - 9x - 2

Answer 1

Polynomials in the fourth degree are called quartic equations. In solving the roots of polynomials, there are techniques available. For quadratic equations, you use the quadratic formula. For cubic equations, you use the scientific calculator. But for quartic equations and higher, it is very complex. The method is very lengthy and can get very messy because you introduce a lot variables. So, I suggest you do the easiest method to estimate the roots.

Graph the equation by plotting arbitrary points. The graph looks like that in the figure. The points at which the curve passes the x-axis are the solution which are encircled in red.In approximation, the rational roots or zero's are -3.73, -1, -0.28 and 2.