What is a polynomial root?

A polynomial root is an input value that makes the corresponding polynomial function evaluate to zero. When working with real numbers, these roots correspond to the x-intercepts of the function's graph. According to the fundamental theorem of algebra, any non-zero polynomial has at most as many roots as its degree.

What we know

• A root of a polynomial is a member of the domain where the function vanishes, producing an output of zero. [1, 2]
• For real-valued functions, the zeros of the polynomial correspond to the x-coordinates where its graph meets the x-axis. [2]
• The fundamental theorem of algebra states that a non-zero polynomial has a number of roots at most equal to its degree. [2]
• All odd-degree polynomials with real coefficients have at least one real root. [4]

Where to go next

• a case in pointWhat is a quadratic equation?
• what followedWhat is the fundamental theorem of algebra?
• the bigger pictureHow are polynomials defined overall?
• compared withHow do cubic functions behave?
• whenWhen were quadratic equations first solved?
• an unexpected connectionHow ancient is the origin of quadratic problems?Solutions to problems framed as quadratic equations were already known as early as 2000 BC, long before modern polynomial notation was established.

Sources

• [1]zero of a function (Wikidata Q214604) · CC0 1.0
• [2]Zero of a function · CC BY-SA 4.0
• [3]Polynomial · CC BY-SA 4.0
• [4]Cubic function · CC BY-SA 4.0
• [5]Quadratic equation · CC BY-SA 4.0