Definition: A root of a function is an x-value at which the y-value is zero.


  • Let y=f(x) be a function. Then x=a is a root if f(a)=0 .
  • If x=a is a root of f(x) , then the graph of f(x) crosses the x-axis at a.
  • So a root is an x-intercept.
  • The x-axis is also the line y=0. So substituting y=0 and solving for x gives roots.

Example: Find the roots of the quadratic function f(x)= x^2-x-2 .

To find the roots of a quadratic function, we use the quadratic formula.

The roots are: x_1=2    and    x_2=-1

That is, this function crosses the x-axis at 2 points: (2,0) and (-1,0).

y=-x+2 y=-x^2+2x-1 y=2^x f(x)=sinx
1 root 1 roots 0 roots infinitely many roots
root: x=2 root: x=1 - roots: \left\{ {x|x = k\pi ,\,\,k \in \bf{Z}} \right\}
linear function quadratic function exponential function? trigonometric function?

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Page last modified on March 14, 2008, at 01:06 AM