How to Solve the Roots of Polynomials

By Vaughnlea Leonard

What is a polynomial?A polynomial is comprised of a collection of monomials, which are expressions or variables of a single term. The root of a polynomial makes the polynomial equal to zero. Figuring out how to solve the roots of polynomials can be an arduous task.

Solve the Roots of Polynomials

Find the degree. You will have to find what degree your polynomial is in. To do this, you just look at the power the leading “x” term is raised to.

Determine the second-degree. If your polynomial is a second-degree equation, or quadratic, you can factor it into a pair of linear functions (a & b), then the zeros will be the numbers that make either function a or b equal to zero. If the quadratic is a perfect linear square in the form of x plus or minus f with that quantity squared equal to d, then the zero will be in the form of x equals plus or minus the square root of d minus or plus f. Also try completing the square. For example, if you have x squared plus bx plus d equals f, then the value of one half of b quantity squared will equal the value of c.

Add a number so your d constant becomes c. For example, if you have the number one and you want to get to three, ask yourself what you would need to do in order to make this happen. This is the same idea. Be sure to treat each side of your equation equally.

Try the quadratic formula. If you find that your quadratic is unfactorable and equal to zero, then the zeroes will be in the form of x=-b plus or minus the square root of b squared minus the quantity of 4ac/2a.

Make a list. Do this by breaking down the problem into roots. If the polynomial is 3rd degree or higher, you have to solve for each root. List the possible real factors. This could be any rational number.

About the Author

Vaughnlea Leonard started her professional writing and editing career in 2005. Her work has appeared in "Press Journal," "Atlantic Publishing Company" and "Hometown News and Florida Today." A former military police enlistee and Florida certified educator, she obtained a Bachelor of Arts in English from the University of Central Florida.