Roots vs Zeroes
A root of an equation is a value at which the equation is satisfied. A polynomial equation may have one or more roots depending on the degree of the polynomial; these roots can be either real or complex. In other forms of equations, roots can be values or functions. “Zeroes” is another term used to call roots of an equation.
For a function of the form f(x)=0 values x1,x2,x3,………xn are the values at which the equation f(x) vanishes. For x1,x2,x3,………xn, the left-hand side of the equation evaluates to zero and the values x1,x2,x3,………xn are called zeroes.
Shown below is the graph of the function f(x)= x3+ x2– 3x – ex
Roots the equation f(x)= x3+ x2– 3x – ex=0 are the x values of the points A, B, C and D. At these points, the value of the function becomes zero; therefore, the roots are called zeroes.