Root  (of a polynomial)

The roots of a polynomial are those values of the variable that cause the polynomial to evaluate to zero.

For example, to find the roots of We are trying find find what value (or values) of x will make it come out to zero. To do this we set the polynomial to zero in the form of an equation: Then we just solve the equation. Add 27 to both sides: Divide through by 3: Take the square root of both sides:

So this polynomial has two roots: positive three, and negative 3. Both will cause the polynomial to have a value of 0.


As shown below, the roots of a polynomial are the values of x that make the polynomial zero, so they are where the graph crosses the x-axis, since this is where the y value (the result of the polynomial) is zero. The roots are the two green dots.

Graph showing the roots of a polynomial

You can interactively explore graphs like this at Quadratic explorer. There, you can adjust the polynomial with sliders to see the effect on the curve and see where the roots come out.

Other quadratic equation topics

Quadratic Function Explorer